Solve x+7/x^2+4x-21*x^2-2x-15/x^2-6x+5

$$\frac { x + 7 } { x ^ { 2 } + 4 x - 21 } \cdot \frac { x ^ { 2 } - 2 x - 15 } { x ^ { 2 } - 6 x + 5 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x+7}{x^{2}+4x-21}.

$$\frac{x+7}{\left(x-3\right)\left(x+7\right)}\times \frac{x^{2}-2x-15}{x^{2}-6x+5}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{1}{x-3}\times \frac{x^{2}-2x-15}{x^{2}-6x+5}$$

Factor the expressions that are not already factored in \frac{x^{2}-2x-15}{x^{2}-6x+5}.

$$\frac{1}{x-3}\times \frac{\left(x-5\right)\left(x+3\right)}{\left(x-5\right)\left(x-1\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{1}{x-3}\times \frac{x+3}{x-1}$$

Multiply \frac{1}{x-3} times \frac{x+3}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Use the distributive property to multiply x-3 by x-1 and combine like terms.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x+7}{x^{2}+4x-21}.

$$\frac{x+7}{\left(x-3\right)\left(x+7\right)}\times \frac{x^{2}-2x-15}{x^{2}-6x+5}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{1}{x-3}\times \frac{x^{2}-2x-15}{x^{2}-6x+5}$$

Factor the expressions that are not already factored in \frac{x^{2}-2x-15}{x^{2}-6x+5}.

$$\frac{1}{x-3}\times \frac{\left(x-5\right)\left(x+3\right)}{\left(x-5\right)\left(x-1\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{1}{x-3}\times \frac{x+3}{x-1}$$

Multiply \frac{1}{x-3} times \frac{x+3}{x-1} by multiplying numerator times numerator and denominator times denominator.

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

Use the distributive property to multiply x-3 by x-1 and combine like terms.

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