How do you simplify #(5x)/(x^2-9)-(4x)/(x^2+5x+6#?

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Answer 1 · 2016-12-15T19:30:11

#(x(x + 22))/((x + 2)(x + 3)(x - 3))

First step to solving this problem is to factor the quadratic equations in the denominators of the two fraction:

#(5x)/((x + 3)(x - 3)) - (4x)/((x + 3)(x + 2))#

To get these fractions over a common denominator we need to multiply each fraction by the appropriate form of #1#:

#((x + 2)/(x + 2) * (5x)/((x + 3)(x - 3))) - ((x - 3)/(x - 3 )* (4x)/((x + 3)(x + 2)))#

#(5x^2 + 10x)/((x + 2)(x + 3)(x - 3)) - (4x^2 - 12x)/((x + 2)(x + 3)(x - 3))#

#(5x^2 + 10x - 4x^2 + 12x)/((x + 2)(x + 3)(x - 3))#

#(x^2 + 22x)/((x + 2)(x + 3)(x - 3))#

#(x(x + 22))/((x + 2)(x + 3)(x - 3))#