What is 3/(x^2-49)-1/(7-x) ?

The solution to 3/(x^2-49)-1/(7-x) is (x+10)/((x-7)(x+7))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3/(x^2-49)-1/(7-x)

simplify

\frac{3}{x ^{2} - 49} - \frac{1}{7 - x}

\frac{x + 10}{( x - 7 ) ( x + 7 )}

Solution steps

\frac{3}{x ^{2} - 49} - \frac{1}{7 - x}

Least Common Multiplier of

x^{2} - 49, 7 - x : (x + 7) (x - 7) (- x + 7)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Apply rule:

a - (- b) = a + b

3 (- x + 7) - (- (x + 7) (- x + 7)) = 3 (- x + 7) + (x + 7) (- x + 7)

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

Simplify

3 (- x + 7) + (x + 7) (- x + 7) : - 3 x + 70 - x^{2}

= \frac{- 3 x + 70 - x ^{2}}{( x + 7 ) ( x - 7 ) ( - x + 7 )}

Cancel

\frac{- 3 x + 70 - x ^{2}}{( x + 7 ) ( x - 7 ) ( - x + 7 )} : \frac{x + 10}{( x - 7 ) ( x + 7 )}

= \frac{x + 10}{( x - 7 ) ( x + 7 )}

\frac{2}{7} x + x

(3 n - 4) (3)

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

6 x^{2} - 13 x + 7

\frac{( 3 - i )}{4 + 2 i}

What is 3/(x^2-49)-1/(7-x) ?
The solution to 3/(x^2-49)-1/(7-x) is (x+10)/((x-7)(x+7))