How do you add $\frac { 7} { x + 2} + \frac { - 4} { x - 3}$ ?

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Answer 1 · 2017-10-02T02:41:29

$=(3x-29)/((x+2)(x-3))$

Find the least common denominator which is $(x+2)(x-3)$

Next, we manipulate each fraction

$(7color(red)((x-3)))/((x+2)(x-3))+(-4color(blue)((x+2)))/((x+2)(x-3))$

$=(7x-21)/((x+2)(x-3))+(-4x-8)/((x+2)(x-3))$

$=(7x-21-4x-8)/((x+2)(x-3))$

Identify and combine like terms to simplify:

$=(color(red)(7x)color(blue)(-21)color(red)(-4x)color(blue)(-8))/((x+2)(x-3))$

$=(3x-29)/((x+2)(x-3))$

Answer 2 · 2017-10-02T02:49:52

$(3x-29)/((x+2)(x-3)$

$lcm$ for $(x+2) & (x-3)$ is $(x+2)*(x-3)$

$(7/(x+2))-(4/(x-3))=((7*(x-3))-(4*(x+2)))/((x+2)*(x-3))$

$=(7x-21-4x-8)/(x^2-x-6)$
$(3x-29)/((x+2)*(x-3))$

How do you add \frac { 7} { x + 2} + \frac { - 4} { x - 3}\frac { 7} { x + 2} + \frac { - 4} { x - 3}?