What is x/(1-x)+3/(2x+3) ?

The solution to x/(1-x)+3/(2x+3) is (2x^2+3)/((-x+1)(2x+3))

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simplify x/(1-x)+3/(2x+3)

simplify

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

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

Solution steps

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

Least Common Multiplier of

1 - x, 2 x + 3 : (- x + 1) (2 x + 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x (2 x + 3) + 3 (- x + 1) : 2 x^{2} + 3

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

r^{9} - 1000 s^{12}

- 10 \cdot 5

- (- 1)^{- 1}

(2 x^{2} - x - 3)^{2}

\frac{1}{20}

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