SOLUTION: finding the sum of algebraic expressions. 1. 3x/2x-3 + x/2x+3= -hope you can help me .. thanks.

Question 346812: finding the sum of algebraic expressions.
1. 3x/2x-3 + x/2x+3=

-hope you can help me ..
thanks.
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
(3x)/(2x-3)+(x)/(2x+3)
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of (2x-3)(2x+3). The (3x)/((2x-3)) expression needs to be multiplied by ((2x+3))/((2x+3)) to make the denominator (2x-3)(2x+3). The (x)/((2x+3)) expression needs to be multiplied by ((2x-3))/((2x-3)) to make the denominator (2x-3)(2x+3).
(3x)/(2x-3)*(2x+3)/(2x+3)+(x)/(2x+3)*(2x-3)/(2x-3)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (2x-3)(2x+3).
(3x(2x+3))/((2x-3)(2x+3))+(x)/(2x+3)*(2x-3)/(2x-3)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (2x-3)(2x+3).
(3x(2x+3))/((2x-3)(2x+3))+(x(2x-3))/((2x-3)(2x+3))
The numerators of expressions that have equal denominators can be combined. In this case, (3x(2x+3))/((2x-3)(2x+3)) and ((x(2x-3)))/((2x-3)(2x+3)) have the same denominator of (2x-3)(2x+3), so the numerators can be combined.
(3x(2x+3)+(x(2x-3)))/((2x-3)(2x+3))
Simplify the numerator of the expression.
(6x^(2)+9x+2x^(2)-3x)/((2x-3)(2x+3))
Combine all similar terms in the polynomial 6x^(2)+9x+2x^(2)-3x.
(8x^(2)+6x)/((2x-3)(2x+3))
Factor out the GCF of 2x from each term in the polynomial.
(2x(4x)+2x(3))/((2x-3)(2x+3))
Factor out the GCF of 2x from 8x^(2)+6x.
(2x(4x+3))/((2x-3)(2x+3))
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