Solve bquadx^2-3x-10/x^2+2x-35*x^2+4x-21/x^2+9x+14

$$b \quad \frac { x ^ { 2 } - 3 x - 10 } { x ^ { 2 } + 2 x - 35 } \cdot \frac { x ^ { 2 } + 4 x - 21 } { x ^ { 2 } + 9 x + 14 }$$

Evaluate

$$\frac{b\left(x-3\right)}{x+7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-3x-10}{x^{2}+2x-35}.

$$b\times \frac{\left(x-5\right)\left(x+2\right)}{\left(x-5\right)\left(x+7\right)}\times \frac{x^{2}+4x-21}{x^{2}+9x+14}$$

Cancel out x-5 in both numerator and denominator.

$$b\times \frac{x+2}{x+7}\times \frac{x^{2}+4x-21}{x^{2}+9x+14}$$

Factor the expressions that are not already factored in \frac{x^{2}+4x-21}{x^{2}+9x+14}.

$$b\times \frac{x+2}{x+7}\times \frac{\left(x-3\right)\left(x+7\right)}{\left(x+2\right)\left(x+7\right)}$$

Cancel out x+7 in both numerator and denominator.

$$b\times \frac{x+2}{x+7}\times \frac{x-3}{x+2}$$

Express b\times \frac{x+2}{x+7} as a single fraction.

$$\frac{b\left(x+2\right)}{x+7}\times \frac{x-3}{x+2}$$

Multiply \frac{b\left(x+2\right)}{x+7} times \frac{x-3}{x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b\left(x+2\right)\left(x-3\right)}{\left(x+7\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{b\left(x-3\right)}{x+7}$$

Use the distributive property to multiply b by x-3.

$$\frac{bx-3b}{x+7}$$

Expand

$$\frac{bx-3b}{x+7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-3x-10}{x^{2}+2x-35}.

$$b\times \frac{\left(x-5\right)\left(x+2\right)}{\left(x-5\right)\left(x+7\right)}\times \frac{x^{2}+4x-21}{x^{2}+9x+14}$$

Cancel out x-5 in both numerator and denominator.

$$b\times \frac{x+2}{x+7}\times \frac{x^{2}+4x-21}{x^{2}+9x+14}$$

Factor the expressions that are not already factored in \frac{x^{2}+4x-21}{x^{2}+9x+14}.

$$b\times \frac{x+2}{x+7}\times \frac{\left(x-3\right)\left(x+7\right)}{\left(x+2\right)\left(x+7\right)}$$

Cancel out x+7 in both numerator and denominator.

$$b\times \frac{x+2}{x+7}\times \frac{x-3}{x+2}$$

Express b\times \frac{x+2}{x+7} as a single fraction.

$$\frac{b\left(x+2\right)}{x+7}\times \frac{x-3}{x+2}$$

Multiply \frac{b\left(x+2\right)}{x+7} times \frac{x-3}{x+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{b\left(x+2\right)\left(x-3\right)}{\left(x+7\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{b\left(x-3\right)}{x+7}$$

Use the distributive property to multiply b by x-3.

$$\frac{bx-3b}{x+7}$$