What is (7x)/(x^2+6x+9)+1/(x^2-9) ?

The solution to (7x)/(x^2+6x+9)+1/(x^2-9) is (7x^2-20x+3)/((x+3)^2(x-3))

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simplify (7x)/(x^2+6x+9)+1/(x^2-9)

simplify

\frac{7 x}{x ^{2} + 6 x + 9} + \frac{1}{x ^{2} - 9}

\frac{7 x ^{2} - 20 x + 3}{( x + 3 ) ^{2} ( x - 3 )}

Solution steps

\frac{7 x}{x ^{2} + 6 x + 9} + \frac{1}{x ^{2} - 9}

Least Common Multiplier of

x^{2} + 6 x + 9, x^{2} - 9 : (x + 3)^{2} (x - 3)

Adjust Fractions based on the LCM

= \frac{7 x ( x - 3 )}{( x + 3 ) ^{2} ( x - 3 )} + \frac{x + 3}{( x + 3 ) ^{2} ( x - 3 )}

Apply the fraction rule:

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

= \frac{7 x ( x - 3 ) + x + 3}{( x + 3 ) ^{2} ( x - 3 )}

Simplify

7 x (x - 3) + x + 3 : 7 x^{2} - 20 x + 3

= \frac{7 x ^{2} - 20 x + 3}{( x + 3 ) ^{2} ( x - 3 )}

(- 1 + 4 i) (9 - 4 i)

50 \times 3

23 \cdot 223

(x + n)^{2}

1040

What is (7x)/(x^2+6x+9)+1/(x^2-9) ?
The solution to (7x)/(x^2+6x+9)+1/(x^2-9) is (7x^2-20x+3)/((x+3)^2(x-3))