What is 4/(3x^2+15x)+(7x)/(x^2+10x+25) ?

The solution to 4/(3x^2+15x)+(7x)/(x^2+10x+25) is (4x+20+21x^2)/(3x(x+5)^2)

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simplify 4/(3x^2+15x)+(7x)/(x^2+10x+25)

simplify

\frac{4}{3 x ^{2} + 15 x} + \frac{7 x}{x ^{2} + 10 x + 25}

\frac{4 x + 20 + 21 x ^{2}}{3 x ( x + 5 ) ^{2}}

Solution steps

\frac{4}{3 x ^{2} + 15 x} + \frac{7 x}{x ^{2} + 10 x + 25}

Least Common Multiplier of

3 x^{2} + 15 x, x^{2} + 10 x + 25 : 3 x (x + 5)^{2}

Adjust Fractions based on the LCM

= \frac{4 ( x + 5 )}{3 x ( x + 5 ) ^{2}} + \frac{21 x ^{2}}{3 x ( x + 5 ) ^{2}}

Apply the fraction rule:

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

= \frac{4 ( x + 5 ) + 21 x ^{2}}{3 x ( x + 5 ) ^{2}}

Simplify

4 (x + 5) + 21 x^{2} : 4 x + 20 + 21 x^{2}

= \frac{4 x + 20 + 21 x ^{2}}{3 x ( x + 5 ) ^{2}}

- 6 x - 6 x

\frac{1 - \frac{1}{x ^{2}}}{3 + \frac{3}{x}}

(x - 7) (x + 9)

(x - 7) (x + 8)

\frac{1}{2} ln (4)

What is 4/(3x^2+15x)+(7x)/(x^2+10x+25) ?
The solution to 4/(3x^2+15x)+(7x)/(x^2+10x+25) is (4x+20+21x^2)/(3x(x+5)^2)