What is 7/(x^2-10x+16)+(2x)/(x^2-13x+40) ?

The solution to 7/(x^2-10x+16)+(2x)/(x^2-13x+40) is (2x^2+3x-35)/((x-2)(x-8)(x-5))

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simplify 7/(x^2-10x+16)+(2x)/(x^2-13x+40)

simplify

\frac{7}{x ^{2} - 10 x + 16} + \frac{2 x}{x ^{2} - 13 x + 40}

\frac{2 x ^{2} + 3 x - 35}{( x - 2 ) ( x - 8 ) ( x - 5 )}

Solution steps

\frac{7}{x ^{2} - 10 x + 16} + \frac{2 x}{x ^{2} - 13 x + 40}

Least Common Multiplier of

x^{2} - 10 x + 16, x^{2} - 13 x + 40 : (x - 2) (x - 8) (x - 5)

Adjust Fractions based on the LCM

= \frac{7 ( x - 5 )}{( x - 2 ) ( x - 8 ) ( x - 5 )} + \frac{2 x ( x - 2 )}{( x - 2 ) ( x - 8 ) ( x - 5 )}

Apply the fraction rule:

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

= \frac{7 ( x - 5 ) + 2 x ( x - 2 )}{( x - 2 ) ( x - 8 ) ( x - 5 )}

Simplify

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

= \frac{2 x ^{2} + 3 x - 35}{( x - 2 ) ( x - 8 ) ( x - 5 )}

12 \div \frac{2}{3}

(x + 5 y)^{3}

\frac{1}{s + 1} + 2

(s + 3)^{3}

\frac{x + 1}{x ^{2} - 1} - \frac{2}{x - 1}

What is 7/(x^2-10x+16)+(2x)/(x^2-13x+40) ?
The solution to 7/(x^2-10x+16)+(2x)/(x^2-13x+40) is (2x^2+3x-35)/((x-2)(x-8)(x-5))