What is expand 2/(x-3)+3/(x+2)-(4x-7)/(x^2-x-6) ?

The solution to expand 2/(x-3)+3/(x+2)-(4x-7)/(x^2-x-6) is 1/(x-3)

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expand 2/(x-3)+3/(x+2)-(4x-7)/(x^2-x-6)

expand

\frac{2}{x - 3} + \frac{3}{x + 2} - \frac{4 x - 7}{x ^{2} - x - 6}

\frac{1}{x - 3}

Solution steps

\frac{2}{x - 3} + \frac{3}{x + 2} - \frac{4 x - 7}{x ^{2} - x - 6}

Factor

x^{2} - x - 6 : (x + 2) (x - 3)

= \frac{2}{x - 3} + \frac{3}{x + 2} - \frac{4 x - 7}{( x + 2 ) ( x - 3 )}

Least Common Multiplier of

x - 3, x + 2, (x + 2) (x - 3) : (x - 3) (x + 2)

Adjust Fractions based on the LCM

= \frac{2 ( x + 2 )}{( x - 3 ) ( x + 2 )} + \frac{3 ( x - 3 )}{( x + 2 ) ( x - 3 )} - \frac{4 x - 7}{( x - 3 ) ( x + 2 )}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 ( x + 2 ) + 3 ( x - 3 ) - ( 4 x - 7 )}{( x - 3 ) ( x + 2 )}

Expand

(x - 3) (x + 2) : x^{2} - x - 6

= \frac{2 ( x + 2 ) + 3 ( x - 3 ) - ( 4 x - 7 )}{x ^{2} - x - 6}

Expand

2 (x + 2) + 3 (x - 3) - (4 x - 7) : x + 2

= \frac{x + 2}{x ^{2} - x - 6}

Factor

x^{2} - x - 6 : (x + 2) (x - 3)

= \frac{x + 2}{( x + 2 ) ( x - 3 )}

Cancel the common factor:

x + 2

= \frac{1}{x - 3}

\frac{90 s ^{4} + 2430 - 270 s ^{2}}{( s ^{2} + 9 ) ^{4}}

(4 x y^{2} - 9 y) d y

a (16, - 17, 0, 0) + b (1, - 1, 16, 17) + c (0, 0, - 1, - 1)

\frac{s ^{2} + 400 \cdot s + 31000}{5 \cdot ( s + 200 ) ^{2}}

\frac{w ^{2}}{s ( s ^{2} + 2 z w s + w ^{2} )}

What is expand 2/(x-3)+3/(x+2)-(4x-7)/(x^2-x-6) ?
The solution to expand 2/(x-3)+3/(x+2)-(4x-7)/(x^2-x-6) is 1/(x-3)