Solve x(x+1)/x+3divx+1/x+3

$$\frac { x ( x + 1 ) } { x + 3 } \div \frac { x + 1 } { x + 3 }$$

Evaluate

$$x$$

Solution Steps

Divide \frac{x\left(x+1\right)}{x+3} by \frac{x+1}{x+3} by multiplying \frac{x\left(x+1\right)}{x+3} by the reciprocal of \frac{x+1}{x+3}.

$$\frac{x\left(x+1\right)\left(x+3\right)}{\left(x+3\right)\left(x+1\right)}$$

Cancel out \left(x+1\right)\left(x+3\right) in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Divide \frac{x\left(x+1\right)}{x+3} by \frac{x+1}{x+3} by multiplying \frac{x\left(x+1\right)}{x+3} by the reciprocal of \frac{x+1}{x+3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+1\right)\left(x+3\right)}{\left(x+3\right)\left(x+1\right)})$$

Cancel out \left(x+1\right)\left(x+3\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.

$$1$$