What is the answer to (ax^3+2x)/(x+1)=x^2-x ?

The answer to (ax^3+2x)/(x+1)=x^2-x is x=0,x=isqrt(3/(-1+a)),x=-isqrt(3/(-1+a));\quad a\ne 1

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(ax^3+2x)/(x+1)=x^2-x

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

x = 0, x = i \frac{3}{- 1 + a}, x = - i \frac{3}{- 1 + a}; a \neq = 1

Solution steps

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

Multiply both sides by

x + 1

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

Solve

a x^{3} + 2 x = x^{2} (x + 1) - x (x + 1) : x = 0, x = i \frac{3}{- 1 + a}, x = - i \frac{3}{- 1 + a}; a \neq = 1

x = 0, x = i \frac{3}{- 1 + a}, x = - i \frac{3}{- 1 + a}; a \neq = 1

Verify Solutions

Find undefined (singularity) points:

x = - 1

Combine undefined points with solutions:

x = 0, x = i \frac{3}{- 1 + a}, x = - i \frac{3}{- 1 + a}; a \neq = 1

\frac{3}{4} = \frac{8}{x}

\frac{25}{35} = \frac{12}{x}

(x - 2) (\frac{800}{x} + 20) = 800

\frac{1}{R} = \frac{R ^{1} + R ^{2}}{R ^{1} R ^{2}}

\frac{8}{3} = \frac{2 x}{3 x - 15}

What is the answer to (ax^3+2x)/(x+1)=x^2-x ?
The answer to (ax^3+2x)/(x+1)=x^2-x is x=0,x=isqrt(3/(-1+a)),x=-isqrt(3/(-1+a));\quad a\ne 1