What is (x+2)/(x+3)+(x+1)/(x^2+6x+9) ?

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

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simplify (x+2)/(x+3)+(x+1)/(x^2+6x+9)

simplify

\frac{x + 2}{x + 3} + \frac{x + 1}{x ^{2} + 6 x + 9}

\frac{x ^{2} + 6 x + 7}{( x + 3 ) ^{2}}

Solution steps

\frac{x + 2}{x + 3} + \frac{x + 1}{x ^{2} + 6 x + 9}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{( x + 2 ) ( x + 3 )}{( x + 3 ) ^{2}} + \frac{x + 1}{( x + 3 ) ^{2}}

Apply the fraction rule:

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

= \frac{( x + 2 ) ( x + 3 ) + x + 1}{( x + 3 ) ^{2}}

Simplify

(x + 2) (x + 3) + x + 1 : x^{2} + 6 x + 7

= \frac{x ^{2} + 6 x + 7}{( x + 3 ) ^{2}}

14 \times 4

- 10 - 1

- 16 + 4

(2 x^{5})^{2}

\frac{6 x}{2 x + 3} + \frac{9}{2 x + 3}

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