What is (x-5)/(x^2+10x+16)+(5x+1)/(x^2+7x+10) ?

The solution to (x-5)/(x^2+10x+16)+(5x+1)/(x^2+7x+10) is (6x^2+41x-17)/((x+2)(x+8)(x+5))

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simplify (x-5)/(x^2+10x+16)+(5x+1)/(x^2+7x+10)

simplify

\frac{x - 5}{x ^{2} + 10 x + 16} + \frac{5 x + 1}{x ^{2} + 7 x + 10}

\frac{6 x ^{2} + 41 x - 17}{( x + 2 ) ( x + 8 ) ( x + 5 )}

Solution steps

\frac{x - 5}{x ^{2} + 10 x + 16} + \frac{5 x + 1}{x ^{2} + 7 x + 10}

Least Common Multiplier of

x^{2} + 10 x + 16, x^{2} + 7 x + 10 : (x + 2) (x + 8) (x + 5)

Adjust Fractions based on the LCM

= \frac{( x - 5 ) ( x + 5 )}{( x + 2 ) ( x + 8 ) ( x + 5 )} + \frac{( 5 x + 1 ) ( x + 8 )}{( x + 2 ) ( x + 8 ) ( x + 5 )}

Apply the fraction rule:

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

= \frac{( x - 5 ) ( x + 5 ) + ( 5 x + 1 ) ( x + 8 )}{( x + 2 ) ( x + 8 ) ( x + 5 )}

Simplify

(x - 5) (x + 5) + (5 x + 1) (x + 8) : 6 x^{2} + 41 x - 17

= \frac{6 x ^{2} + 41 x - 17}{( x + 2 ) ( x + 8 ) ( x + 5 )}

9 1^{2}

\frac{( \frac{1}{6} + \frac{3}{7} )}{( \frac{2}{3} ) ^{2} + \frac{1}{5} - 1}

8^{2} + 7^{2}

(1 + tan^{2} (u)) (1 - sin^{2} (u))

3 lo g_{10} (x) + 2 lo g_{10} (z^{5}) - lo g_{10} (y)

What is (x-5)/(x^2+10x+16)+(5x+1)/(x^2+7x+10) ?
The solution to (x-5)/(x^2+10x+16)+(5x+1)/(x^2+7x+10) is (6x^2+41x-17)/((x+2)(x+8)(x+5))