Solve x^2-4x+3/x^2-9divx-1/x^2+3x

$$\frac { x ^ { 2 } - 4 x + 3 } { x ^ { 2 } - 9 } \div \frac { x - 1 } { x ^ { 2 } + 3 x }$$

Evaluate

$$x$$

Short Solution Steps

Divide \frac{x^{2}-4x+3}{x^{2}-9} by \frac{x-1}{x^{2}+3x} by multiplying \frac{x^{2}-4x+3}{x^{2}-9} by the reciprocal of \frac{x-1}{x^{2}+3x}.

$$\frac{\left(x^{2}-4x+3\right)\left(x^{2}+3x\right)}{\left(x^{2}-9\right)\left(x-1\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\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^{2}-4x+3}{x^{2}-9} by \frac{x-1}{x^{2}+3x} by multiplying \frac{x^{2}-4x+3}{x^{2}-9} by the reciprocal of \frac{x-1}{x^{2}+3x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x^{2}-4x+3\right)\left(x^{2}+3x\right)}{\left(x^{2}-9\right)\left(x-1\right)})$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-4x+3\right)\left(x^{2}+3x\right)}{\left(x^{2}-9\right)\left(x-1\right)}.

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

Cancel out \left(x-3\right)\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.

$$1$$