What is (3x-1)/(x^2-5x-6)-2/(6-x) ?

The solution to (3x-1)/(x^2-5x-6)-2/(6-x) is (5x+1)/((x-6)(x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (3x-1)/(x^2-5x-6)-2/(6-x)

simplify

\frac{3 x - 1}{x ^{2} - 5 x - 6} - \frac{2}{6 - x}

\frac{5 x + 1}{( x - 6 ) ( x + 1 )}

Solution steps

\frac{3 x - 1}{x ^{2} - 5 x - 6} - \frac{2}{6 - x}

Least Common Multiplier of

x^{2} - 5 x - 6, 6 - x : (x + 1) (x - 6) (- x + 6)

Adjust Fractions based on the LCM

= \frac{( 3 x - 1 ) ( - x + 6 )}{( x + 1 ) ( x - 6 ) ( - x + 6 )} - \frac{- 2 ( x + 1 ) ( - x + 6 )}{( x + 1 ) ( x - 6 ) ( - x + 6 )}

Apply the fraction rule:

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

= \frac{( 3 x - 1 ) ( - x + 6 ) - ( - 2 ( x + 1 ) ( - x + 6 ) )}{( x + 1 ) ( x - 6 ) ( - x + 6 )}

Apply rule:

a - (- b) = a + b

(3 x - 1) (- x + 6) - (- 2 (x + 1) (- x + 6)) = (3 x - 1) (- x + 6) + 2 (x + 1) (- x + 6)

= \frac{( 3 x - 1 ) ( - x + 6 ) + 2 ( x + 1 ) ( - x + 6 )}{( x + 1 ) ( x - 6 ) ( - x + 6 )}

Simplify

(3 x - 1) (- x + 6) + 2 (x + 1) (- x + 6) : - 5 x^{2} + 29 x + 6

= \frac{- 5 x ^{2} + 29 x + 6}{( x + 1 ) ( x - 6 ) ( - x + 6 )}

Cancel

\frac{- 5 x ^{2} + 29 x + 6}{( x + 1 ) ( x - 6 ) ( - x + 6 )} : \frac{5 x + 1}{( x - 6 ) ( x + 1 )}

= \frac{5 x + 1}{( x - 6 ) ( x + 1 )}

6 \times 50

\frac{5}{6} + \frac{1}{12}

\frac{480}{600}

9600

147 + 192

What is (3x-1)/(x^2-5x-6)-2/(6-x) ?
The solution to (3x-1)/(x^2-5x-6)-2/(6-x) is (5x+1)/((x-6)(x+1))