<PRE><B>Question 343346</B>
((a)/(b)+(c)/(d))/(e)

To add fractions, the denominators must be equal.  The denominators can be made equal by finding the least common denominator (LCD).  In this case, the LCD is bd.  Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
((a)/(b)*(d)/(d)+(c)/(d)*(b)/(b))/(e)

Complete the multiplication to produce a denominator of bd in each expression.
((ad)/(bd)+(bc)/(bd))/(e)

Combine the numerators of all expressions that have common denominators.
((ad+bc)/(bd))/(e)

Multiply e by bd to get bde.
(ad+bc)/(bde)



(3*x^(-2)*y-2*a*b^(-1))/(x)

Remove the negative exponent in the numerator by rewriting x^(-2) as (1)/(x^(2)).  A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
(3*(1)/(x^(2))*y-2*a*b^(-1))/(x)

Remove the negative exponent in the numerator by rewriting b^(-1) as (1)/(b).  A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
(3*(1)/(x^(2))*y-2*a*(1)/(b))/(x)

Multiply 3 by (1)/(x^(2)) to get (3)/(x^(2)).
((3)/(x^(2))*y-2*a*(1)/(b))/(x)

Multiply (3)/(x^(2)) by y to get (3y)/(x^(2)).
((3y)/(x^(2))-2*a*(1)/(b))/(x)

Multiply -2 by a to get -2a.
((3y)/(x^(2))-2a*(1)/(b))/(x)

Multiply -2a by (1)/(b) to get -(2a)/(b).
((3y)/(x^(2))-(2a)/(b))/(x)

To add fractions, the denominators must be equal.  The denominators can be made equal by finding the least common denominator (LCD).  In this case, the LCD is x^(2)b.  Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
((3y)/(x^(2))*(b)/(b)-(2a)/(b)*(x^(2))/(x^(2)))/(x)

Complete the multiplication to produce a denominator of x^(2)b in each expression.
((3by)/(bx^(2))-(2ax^(2))/(bx^(2)))/(x)

Combine the numerators of all expressions that have common denominators.
((3by-2ax^(2))/(bx^(2)))/(x)

Multiply x by bx^(2) to get bx^(3).
(3by-2ax^(2))/(bx^(3))



((x+2)*(1)/(2)*((x+1)^(-1))/(2)*(x+1)/(2))/((x+2)^(2))

Multiply the rational expressions to get (1)/(2(x+1)).
((x+2)*(1)/(2)*(1)/(2(x+1))*(x+1)/(2))/((x+2)^(2))

Multiply 2 by 2 to get 4.
((x+2)/((4)(x+1))*(x+1)/(2))/((x+2)^(2))

Reduce the expression by canceling out the common factor of (x+1) from the numerator and denominator.
((((x+2)&lt;X&gt;(x+1)&lt;x&gt;)/(2(4)&lt;X&gt;(x+1)&lt;x&gt;)))/((x+2)^(2))

Reduce the expression by canceling out the common factor of (x+1) from the numerator and denominator.
((x+2)/(2(4)))/((x+2)^(2))

Multiply 2 by 4 to get 8.
((x+2)/(2*4))/((x+2)^(2))

Multiply 2 by 4 to get 8.
((x+2)/(8))/((x+2)^(2))

Cancel the common factor of (x+2) from the denominator of the first expression and the numerator of the second expression.
(1)/(x+2)*(1)/(8)

Multiply the rational expressions to get (1)/(8(x+2)).
(1)/(8(x+2))



((3*x-1)/(2)*2-(2*x+3)*(1)/(2)*((3*x-1)^(-1))/(2))/(3)*x-1

Multiply 3 by x to get 3x.
((3x-1)/(2)*2-(2*x+3)*(1)/(2)*((3*x-1)^(-1))/(2))/(3)*x-1

Multiply 2 by x to get 2x.
((3x-1)/(2)*2-(2x+3)*(1)/(2)*((3*x-1)^(-1))/(2))/(3)*x-1

Multiply 3 by x to get 3x.
((3x-1)/(2)*2-(2x+3)*(1)/(2)*((3x-1)^(-1))/(2))/(3)*x-1

Multiply the rational expressions to get (1)/(2(3x-1)).
((3x-1)/(2)*2-(2x+3)*(1)/(2)*(1)/(2(3x-1)))/(3)*x-1

Cancel the common factor of 2 from the denominator of the first expression and the numerator of the second expression.
((3x-1)-(2x+3)*(1)/(2)*(1)/(2(3x-1)))/(3)*x-1

Multiply 2 by 2 to get 4.
((3x-1)-(2x+3)/((4)(3x-1)))/(3)*x-1

Remove the parentheses around the 4 in the denominator.
((3x-1)-(2x+3)/(4(3x-1)))/(3)*x-1

Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 4(3x-1).
((3x*(4(3x-1))/(4(3x-1))-1*(4(3x-1))/(4(3x-1))-(2x+3)/(4(3x-1))))/(3)*x-1

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4(3x-1).
(((3x*4(3x-1))/(4(3x-1))-1*(4(3x-1))/(4(3x-1))-(2x+3)/(4(3x-1))))/(3)*x-1

Multiply 3x by 4 to get 12x.
(((12x(3x-1))/(4(3x-1))-1*(4(3x-1))/(4(3x-1))-(2x+3)/(4(3x-1))))/(3)*x-1

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4(3x-1).
(((12x(3x-1))/(4(3x-1))-(1*4(3x-1))/(4(3x-1))-(2x+3)/(4(3x-1))))/(3)*x-1

Multiply 1 by 4(3x-1) to get 4(3x-1).
(((12x(3x-1))/(4(3x-1))-(4(3x-1))/(4(3x-1))-(2x+3)/(4(3x-1))))/(3)*x-1

The numerators of expressions that have equal denominators can be combined.  In this case, ((12x(3x-1)))/(4(3x-1)) and -((4(3x-1)))/(4(3x-1)) have the same denominator of 4(3x-1), so the numerators can be combined.
((((12x(3x-1))-(4(3x-1))-(2x+3))/(4(3x-1))))/(3)*x-1

Simplify the numerator of the expression.
((36x^(2)-12x-12x+4-2x-3)/(4(3x-1)))/(3)*x-1

Combine all similar terms in the polynomial 36x^(2)-12x-12x+4-2x-3.
((36x^(2)-26x+1)/(4(3x-1)))/(3)*x-1

Multiply 3 by 4 to get 12.
(36x^(2)-26x+1)/((12)(3x-1))*x-1

Remove the parentheses around the 12 in the denominator.
(36x^(2)-26x+1)/(12(3x-1))*x-1

Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 12(3x-1).
(x(36x^(2)-26x+1))/(12(3x-1))-1*(12(3x-1))/(12(3x-1))

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 12(3x-1).
(x(36x^(2)-26x+1))/(12(3x-1))-(1*12(3x-1))/(12(3x-1))

Multiply 1 by 12(3x-1) to get 12(3x-1).
(x(36x^(2)-26x+1))/(12(3x-1))-(12(3x-1))/(12(3x-1))

The numerators of expressions that have equal denominators can be combined.  In this case, (x(36x^(2)-26x+1))/(12(3x-1)) and -((12(3x-1)))/(12(3x-1)) have the same denominator of 12(3x-1), so the numerators can be combined.
(x(36x^(2)-26x+1)-(12(3x-1)))/(12(3x-1))

Simplify the numerator of the expression.
(36x^(3)-26x^(2)+x-36x+12)/(12(3x-1))

Since x and -36x are like terms, add -36x to x to get -35x.
(36x^(3)-26x^(2)-35x+12)/(12(3x-1))



((x+2)/(3)*3-(3*x-1)*(1)/(3)*((x+2)^(-2))/(3))/((x+2)^(2))/(3)

Multiply 3 by x to get 3x.
((((x+2)/(3)*3-(3x-1)*(1)/(3)*((x+2)^(-2))/(3))/((x+2)^(2))))/(3)

Multiply the rational expressions to get (1)/(3(x+2)^(2)).
((((x+2)/(3)*3-(3x-1)*(1)/(3)*(1)/(3(x+2)^(2)))/((x+2)^(2))))/(3)

Cancel the common factor of 3 from the denominator of the first expression and the numerator of the second expression.
(((x+2)-(3x-1)*(1)/(3)*(1)/(3(x+2)^(2)))/((x+2)^(2)))/(3)

Multiply 3 by 3 to get 9.
((((x+2)-(3x-1)/((9)(x+2)^(2)))/((x+2)^(2))))/(3)

Remove the parentheses around the 9 in the denominator.
((((x+2)-(3x-1)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of 9(x+2)^(2).
(((x*(9(x+2)^(2))/(9(x+2)^(2))+2*(9(x+2)^(2))/(9(x+2)^(2))-(3x-1)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 9(x+2)^(2).
((((x*9(x+2)^(2))/(9(x+2)^(2))+2*(9(x+2)^(2))/(9(x+2)^(2))-(3x-1)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

Multiply x by 9 to get 9x.
((((9x(x+2)^(2))/(9(x+2)^(2))+2*(9(x+2)^(2))/(9(x+2)^(2))-(3x-1)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 9(x+2)^(2).
((((9x(x+2)^(2))/(9(x+2)^(2))+(2*9(x+2)^(2))/(9(x+2)^(2))-(3x-1)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

Multiply 2 by 9 to get 18.
((((9x(x+2)^(2))/(9(x+2)^(2))+(18(x+2)^(2))/(9(x+2)^(2))-(3x-1)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

The numerators of expressions that have equal denominators can be combined.  In this case, ((9x(x+2)^(2)))/(9(x+2)^(2)) and ((18(x+2)^(2)))/(9(x+2)^(2)) have the same denominator of 9(x+2)^(2), so the numerators can be combined.
((((((9x(x+2)^(2))+(18(x+2)^(2))-(3x-1))/(9(x+2)^(2))))/((x+2)^(2))))/(3)

Simplify the numerator of the expression.
((((9x^(3)+54x^(2)+105x+73)/(9(x+2)^(2)))/((x+2)^(2))))/(3)

Combine the two common factors of (x+2)^(2) by adding the exponents.
((9x^(3)+54x^(2)+105x+73)/(9(x+2)^(4)))/(3)

Multiply 3 by 9 to get 27.
(9x^(3)+54x^(2)+105x+73)/((27)(x+2)^(4))

Remove the parentheses around the 27 in the denominator.
(9x^(3)+54x^(2)+105x+73)/(27(x+2)^(4))</PRE>