What is x+3+(x+7)/(2-x) ?

The solution to x+3+(x+7)/(2-x) is (-x^2+13)/(2-x)

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simplify x+3+(x+7)/(2-x)

simplify

x + 3 + \frac{x + 7}{2 - x}

\frac{- x ^{2} + 13}{2 - x}

Solution steps

x + 3 + \frac{x + 7}{2 - x}

Convert

x

to fraction

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

Convert

3

to fraction

: \frac{3 ( 2 - x )}{2 - x}

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

Apply the fraction rule:

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

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

Simplify

x (2 - x) + 3 (2 - x) + x + 7 : - x^{2} + 13

= \frac{- x ^{2} + 13}{2 - x}

3^{- 1} + 3^{- 2} + 3^{- 3} + 3^{- 4}

n (n + 1) (2 n + 1) (3 n^{2} + 3 n - 1)

(x - 4) (2 x + x^{2}) (x - 1)

- 3 - ∣ - 3 ∣

(x^{2})