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

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

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

simplify

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

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

Solution steps

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

Convert

1

to fraction

: \frac{1 - x}{1 - x}

Convert

x

to fraction

: \frac{x ( 1 - x )}{1 - x}

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

Apply the fraction rule:

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

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

Simplify

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

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

\frac{2 a}{5} + \frac{a}{3}

(a + 3 b)^{3}

(x - 3) (4 x + 2)

\frac{8 x ^{3}}{16 x ^{2} - 16 x}

\frac{1}{\frac{s i n ( x )}{c o s ( x )}}