What is 2/(x-7)-7/(x^2-11x+28) ?

The solution to 2/(x-7)-7/(x^2-11x+28) is (2x-15)/((x-7)(x-4))

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simplify 2/(x-7)-7/(x^2-11x+28)

simplify

\frac{2}{x - 7} - \frac{7}{x ^{2} - 11 x + 28}

\frac{2 x - 15}{( x - 7 ) ( x - 4 )}

Solution steps

\frac{2}{x - 7} - \frac{7}{x ^{2} - 11 x + 28}

Least Common Multiplier of

x - 7, x^{2} - 11 x + 28 : (x - 7) (x - 4)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 (x - 4) - 7 : 2 x - 15

= \frac{2 x - 15}{( x - 7 ) ( x - 4 )}

18 \times 4

x^{- 6} + x^{2}

\frac{( x ^{2} - 1 )}{( x - 1 )}

(x + 2) (3 x^{2} - 7 x - 4)

\frac{1}{9} \div \frac{1}{3}

What is 2/(x-7)-7/(x^2-11x+28) ?
The solution to 2/(x-7)-7/(x^2-11x+28) is (2x-15)/((x-7)(x-4))