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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

\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}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\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 )}

Simplify

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

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

Cancel the common factor:

x + 2

= \frac{1}{x - 3}

(n - 1)^{2}

(x y - z) (x y + z)

\frac{lo g _{10} ( 3 )}{lo g _{10} ( 2 )}

- x^{2} - 2 x

5 \cdot (- 4) 20

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