What is (3x)/(5x^2-27x+10)+6/(x^2-2x-15) ?

The solution to (3x)/(5x^2-27x+10)+6/(x^2-2x-15) is (3x^2+39x-12)/((x-5)(x+3)(5x-2))

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simplify (3x)/(5x^2-27x+10)+6/(x^2-2x-15)

simplify

\frac{3 x}{5 x ^{2} - 27 x + 10} + \frac{6}{x ^{2} - 2 x - 15}

\frac{3 x ^{2} + 39 x - 12}{( x - 5 ) ( x + 3 ) ( 5 x - 2 )}

Solution steps

\frac{3 x}{5 x ^{2} - 27 x + 10} + \frac{6}{x ^{2} - 2 x - 15}

Least Common Multiplier of

5 x^{2} - 27 x + 10, x^{2} - 2 x - 15 : (x - 5) (x + 3) (5 x - 2)

Adjust Fractions based on the LCM

= \frac{3 x ( x + 3 )}{( x - 5 ) ( x + 3 ) ( 5 x - 2 )} + \frac{6 ( 5 x - 2 )}{( x - 5 ) ( x + 3 ) ( 5 x - 2 )}

Apply the fraction rule:

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

= \frac{3 x ( x + 3 ) + 6 ( 5 x - 2 )}{( x - 5 ) ( x + 3 ) ( 5 x - 2 )}

Simplify

3 x (x + 3) + 6 (5 x - 2) : 3 x^{2} + 39 x - 12

= \frac{3 x ^{2} + 39 x - 12}{( x - 5 ) ( x + 3 ) ( 5 x - 2 )}

(14 - x)^{2}

- (- 15) - (- 9)

3 \frac{1}{7}

d (arctan (x))

lo g_{1} (100)

What is (3x)/(5x^2-27x+10)+6/(x^2-2x-15) ?
The solution to (3x)/(5x^2-27x+10)+6/(x^2-2x-15) is (3x^2+39x-12)/((x-5)(x+3)(5x-2))