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

The solution to x^2+2x+2+(x+7)/(x^2-2) is (x^4+2x^3-3x+3)/(x^2-2)

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simplify x^2+2x+2+(x+7)/(x^2-2)

simplify

x^{2} + 2 x + 2 + \frac{x + 7}{x ^{2} - 2}

\frac{x ^{4} + 2 x ^{3} - 3 x + 3}{x ^{2} - 2}

Solution steps

x^{2} + 2 x + 2 + \frac{x + 7}{x ^{2} - 2}

Convert

x^{2}

to fraction

: \frac{x ^{2} ( x ^{2} - 2 )}{x ^{2} - 2}

Convert

2 x

to fraction

: \frac{2 x ( x ^{2} - 2 )}{x ^{2} - 2}

Convert

2

to fraction

: \frac{2 ( x ^{2} - 2 )}{x ^{2} - 2}

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

Apply the fraction rule:

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

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

Simplify

x^{2} (x^{2} - 2) + 2 x (x^{2} - 2) + 2 (x^{2} - 2) + x + 7 : x^{4} + 2 x^{3} - 3 x + 3

= \frac{x ^{4} + 2 x ^{3} - 3 x + 3}{x ^{2} - 2}

Γ (\frac{1}{3})

+ (x^{2} - 11 x + 24)

(8 - 6)^{2}

x^{3} x

\frac{2 π}{\frac{1}{10}}

What is x^2+2x+2+(x+7)/(x^2-2) ?
The solution to x^2+2x+2+(x+7)/(x^2-2) is (x^4+2x^3-3x+3)/(x^2-2)