Solve 1-x/a+1*a^2+a/x-x^2*x^2/a

$$\frac { 1 - x } { a + 1 } \cdot \frac { a ^ { 2 } + a } { x - x ^ { 2 } } \cdot \frac { x ^ { 2 } } { a }$$

Evaluate

$$x$$

Short Solution Steps

Multiply \frac{1-x}{a+1} times \frac{a^{2}+a}{x-x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(1-x\right)\left(a^{2}+a\right)}{\left(a+1\right)\left(x-x^{2}\right)}\times \frac{x^{2}}{a}$$

Multiply \frac{\left(1-x\right)\left(a^{2}+a\right)}{\left(a+1\right)\left(x-x^{2}\right)} times \frac{x^{2}}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(1-x\right)\left(a^{2}+a\right)x^{2}}{\left(a+1\right)\left(x-x^{2}\right)a}$$

Factor the expressions that are not already factored.

$$\frac{a\left(a+1\right)\left(-x+1\right)x^{2}}{ax\left(a+1\right)\left(-x+1\right)}$$

Cancel out ax\left(a+1\right)\left(-x+1\right) in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Multiply \frac{1-x}{a+1} times \frac{a^{2}+a}{x-x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(1-x\right)\left(a^{2}+a\right)}{\left(a+1\right)\left(x-x^{2}\right)}\times \frac{x^{2}}{a})$$

Multiply \frac{\left(1-x\right)\left(a^{2}+a\right)}{\left(a+1\right)\left(x-x^{2}\right)} times \frac{x^{2}}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(1-x\right)\left(a^{2}+a\right)x^{2}}{\left(a+1\right)\left(x-x^{2}\right)a})$$

Factor the expressions that are not already factored in \frac{\left(1-x\right)\left(a^{2}+a\right)x^{2}}{\left(a+1\right)\left(x-x^{2}\right)a}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{a\left(a+1\right)\left(-x+1\right)x^{2}}{ax\left(a+1\right)\left(-x+1\right)})$$

Cancel out ax\left(a+1\right)\left(-x+1\right) in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$