What is 1/(x^2-10x+24)-(2x)/(x-6) ?

The solution to 1/(x^2-10x+24)-(2x)/(x-6) is (1-2x^2+8x)/((x-4)(x-6))

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simplify 1/(x^2-10x+24)-(2x)/(x-6)

simplify

\frac{1}{x ^{2} - 10 x + 24} - \frac{2 x}{x - 6}

\frac{1 - 2 x ^{2} + 8 x}{( x - 4 ) ( x - 6 )}

Solution steps

\frac{1}{x ^{2} - 10 x + 24} - \frac{2 x}{x - 6}

Least Common Multiplier of

x^{2} - 10 x + 24, x - 6 : (x - 4) (x - 6)

Adjust Fractions based on the LCM

= \frac{1}{( x - 4 ) ( x - 6 )} - \frac{2 x ( x - 4 )}{( x - 4 ) ( x - 6 )}

Apply the fraction rule:

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

= \frac{1 - 2 x ( x - 4 )}{( x - 4 ) ( x - 6 )}

Simplify

1 - 2 x (x - 4) : 1 - 2 x^{2} + 8 x

= \frac{1 - 2 x ^{2} + 8 x}{( x - 4 ) ( x - 6 )}

\frac{25}{18}

\frac{- 3 x + 7}{2} - \frac{- 2 x - 3}{2}

\frac{- 3 + 1}{2}

10 \cdot 3

(x^{2} + x + 2)^{2}

What is 1/(x^2-10x+24)-(2x)/(x-6) ?
The solution to 1/(x^2-10x+24)-(2x)/(x-6) is (1-2x^2+8x)/((x-4)(x-6))