What is (5x+7)/(x-4)-(3x)/(x^2-9x+20) ?

The solution to (5x+7)/(x-4)-(3x)/(x^2-9x+20) is (5x^2-21x-35)/((x-4)(x-5))

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simplify (5x+7)/(x-4)-(3x)/(x^2-9x+20)

simplify

\frac{5 x + 7}{x - 4} - \frac{3 x}{x ^{2} - 9 x + 20}

\frac{5 x ^{2} - 21 x - 35}{( x - 4 ) ( x - 5 )}

Solution steps

\frac{5 x + 7}{x - 4} - \frac{3 x}{x ^{2} - 9 x + 20}

Least Common Multiplier of

x - 4, x^{2} - 9 x + 20 : (x - 4) (x - 5)

Adjust Fractions based on the LCM

= \frac{( 5 x + 7 ) ( x - 5 )}{( x - 4 ) ( x - 5 )} - \frac{3 x}{( x - 4 ) ( x - 5 )}

Apply the fraction rule:

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

= \frac{( 5 x + 7 ) ( x - 5 ) - 3 x}{( x - 4 ) ( x - 5 )}

Simplify

(5 x + 7) (x - 5) - 3 x : 5 x^{2} - 21 x - 35

= \frac{5 x ^{2} - 21 x - 35}{( x - 4 ) ( x - 5 )}

(2 x - 3) (3 x^{2} + 7 x + 5)

\frac{6}{28}

- 10 + 3

- 2 - 12

- 5 + 12

What is (5x+7)/(x-4)-(3x)/(x^2-9x+20) ?
The solution to (5x+7)/(x-4)-(3x)/(x^2-9x+20) is (5x^2-21x-35)/((x-4)(x-5))