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Question 389323: ADD OR SUBTRACT. SIMPLIFY, FACTOR, CANCEL AND SHOW STEPS FOR FINDING LOWEST COMMON DENOMINATOR. ASSUME NO DENOMINATOR IS 0. I NEED HELP WITH 4 PROBLEMS PLEASE.
A/A^2-4-2/A^2-4
X^2+7X/3+4/9
2X/5Y-3X/4Y
(X+5)2/X^2+2X-15+2/4X-12
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! Please indicate where the problem begins and ends; for example, on the second one, it can be worked several ways. It can be read as 
or 
Use parenthases to show which are together and apart. If any of these are set up incorrectly, please repost them or email me at Jennifer_Sadler@stu.southiniversity.edu. I will be happy to help you step by step.
(A)/(A^(2)-4)-(2)/(A^(2)-4)
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(A)/((A-2)(A+2))-(2)/(A^(2)-4)
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
(A)/((A-2)(A+2))-(2)/((A-2)(A+2))
Combine all similar expressions in the polynomial.
(A-2)/((A-2)(A+2))
Reduce the expression by canceling out the common factor of (A-2) from the numerator and denominator.
((A-2))/((A-2)(A+2))
Reduce the expression by canceling out the common factor of (A-2) from the numerator and denominator.
(1)/(A+2)
(X^(2)+7X)/(3)+(4)/(9)
Factor out the GCF of X from each term in the polynomial.
(X(X)+X(7))/(3)+(4)/(9)
Factor out the GCF of X from X^(2)+7X.
(X(X+7))/(3)+(4)/(9)
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 9. The (X(X+7))/(3) expression needs to be multiplied by ((3))/((3)) to make the denominator 9.
(X(X+7))/(3)*(3)/(3)+(4)/(9)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 9.
(X(X+7)(3))/(9)+(4)/(9)
The numerators of expressions that have equal denominators can be combined. In this case, ((X(X+7)(3)))/(9) and (4)/(9) have the same denominator of 9, so the numerators can be combined.
((X(X+7)(3))+4)/(9)
Simplify the numerator of the expression.
(3X^(2)+21X+4)/(9)
(2X)/(5Y)-(3X)/(4Y)
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 20Y. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(2X)/(5Y)*(4)/(4)-(3X)/(4Y)*(5)/(5)
Complete the multiplication to produce a denominator of 20Y in each expression.
(8X)/(20Y)-(15X)/(20Y)
Combine the numerators of all expressions that have common denominators.
(8X-15X)/(20Y)
Combine all like terms in the numerator.
(-7X)/(20Y)
Move the minus sign from the numerator to the front of the expression.
-(7X)/(20Y)
((X+5)^(2))/(X^(2)+2X)-(15+2)/(4X-12)
Factor out the GCF of X from each term in the polynomial.
((X+5)^(2))/(X(X)+X(2))-(15+2)/(4X-12)
Factor out the GCF of X from X^(2)+2X.
((X+5)^(2))/(X(X+2))-(15+2)/(4X-12)
Add 2 to 15 to get 17.
((X+5)^(2))/(X(X+2))-(17)/(4X-12)
Factor out the GCF of 4 from each term in the polynomial.
((X+5)^(2))/(X(X+2))-(17)/(4(X)+4(-3))
Factor out the GCF of 4 from 4X-12.
((X+5)^(2))/(X(X+2))-(17)/(4(X-3))
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4X(X-3)(X+2). The ((X+5)^(2))/(X(X+2)) expression needs to be multiplied by (4(X-3))/(4(X-3)) to make the denominator 4X(X-3)(X+2). The -(17)/(4(X-3)) expression needs to be multiplied by (X(X+2))/(X(X+2)) to make the denominator 4X(X-3)(X+2).
((X+5)^(2))/(X(X+2))*(4(X-3))/(4(X-3))-(17)/(4(X-3))*(X(X+2))/(X(X+2))
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4X(X-3)(X+2).
((X+5)^(2)*4(X-3))/(4X(X-3)(X+2))-(17)/(4(X-3))*(X(X+2))/(X(X+2))
Multiply (X+5)^(2) by 4(X-3) to get 4(X+5)^(2)(X-3).
(4(X+5)^(2)(X-3))/(4X(X-3)(X+2))-(17)/(4(X-3))*(X(X+2))/(X(X+2))
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4X(X-3)(X+2).
(4(X+5)^(2)(X-3))/(4X(X-3)(X+2))-(17*X(X+2))/(4X(X-3)(X+2))
Multiply 17 by X to get 17X.
(4(X+5)^(2)(X-3))/(4X(X-3)(X+2))-(17X(X+2))/(4X(X-3)(X+2))
The numerators of expressions that have equal denominators can be combined. In this case, ((4(X+5)^(2)(X-3)))/(4X(X-3)(X+2)) and -((17X(X+2)))/(4X(X-3)(X+2)) have the same denominator of 4X(X-3)(X+2), so the numerators can be combined.
((4(X+5)^(2)(X-3))-(17X(X+2)))/(4X(X-3)(X+2))
Simplify the numerator of the expression.
(4X^(3)+11X^(2)-54X-300)/(4X(X-3)(X+2))
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