What is (5x+1)/(x-6)-x/(x^2-10x+24) ?

The solution to (5x+1)/(x-6)-x/(x^2-10x+24) is (5x^2-20x-4)/((x-6)(x-4))

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simplify (5x+1)/(x-6)-x/(x^2-10x+24)

simplify

\frac{5 x + 1}{x - 6} - \frac{x}{x ^{2} - 10 x + 24}

\frac{5 x ^{2} - 20 x - 4}{( x - 6 ) ( x - 4 )}

Solution steps

\frac{5 x + 1}{x - 6} - \frac{x}{x ^{2} - 10 x + 24}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{( 5 x + 1 ) ( x - 4 )}{( x - 6 ) ( x - 4 )} - \frac{x}{( x - 6 ) ( x - 4 )}

Apply the fraction rule:

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

= \frac{( 5 x + 1 ) ( x - 4 ) - x}{( x - 6 ) ( x - 4 )}

Simplify

(5 x + 1) (x - 4) - x : 5 x^{2} - 20 x - 4

= \frac{5 x ^{2} - 20 x - 4}{( x - 6 ) ( x - 4 )}

(12 - i) - (8 - 8 i)

\frac{3}{4} \div 6

1 \frac{1}{8}

x - (x - y)

\frac{1}{4} - \frac{1}{16}

What is (5x+1)/(x-6)-x/(x^2-10x+24) ?
The solution to (5x+1)/(x-6)-x/(x^2-10x+24) is (5x^2-20x-4)/((x-6)(x-4))