Solve 3x^2+3x/x^2+8x+7+3x^2-75/x^2+2x-35

$$\frac { 3 x ^ { 2 } + 3 x } { x ^ { 2 } + 8 x + 7 } + \frac { 3 x ^ { 2 } - 75 } { x ^ { 2 } + 2 x - 35 }$$

Evaluate

$$\frac{3\left(2x+5\right)}{x+7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}+3x}{x^{2}+8x+7}.

$$\frac{3x\left(x+1\right)}{\left(x+1\right)\left(x+7\right)}+\frac{3x^{2}-75}{x^{2}+2x-35}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{3x}{x+7}+\frac{3x^{2}-75}{x^{2}+2x-35}$$

Factor the expressions that are not already factored in \frac{3x^{2}-75}{x^{2}+2x-35}.

$$\frac{3x}{x+7}+\frac{3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+7\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{3x}{x+7}+\frac{3\left(x+5\right)}{x+7}$$

Since \frac{3x}{x+7} and \frac{3\left(x+5\right)}{x+7} have the same denominator, add them by adding their numerators.

$$\frac{3x+3\left(x+5\right)}{x+7}$$

Do the multiplications in 3x+3\left(x+5\right).

$$\frac{3x+3x+15}{x+7}$$

Combine like terms in 3x+3x+15.

$$\frac{6x+15}{x+7}$$

Expand

$$\frac{3\left(2x+5\right)}{x+7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}+3x}{x^{2}+8x+7}.

$$\frac{3x\left(x+1\right)}{\left(x+1\right)\left(x+7\right)}+\frac{3x^{2}-75}{x^{2}+2x-35}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{3x}{x+7}+\frac{3x^{2}-75}{x^{2}+2x-35}$$

Factor the expressions that are not already factored in \frac{3x^{2}-75}{x^{2}+2x-35}.

$$\frac{3x}{x+7}+\frac{3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+7\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{3x}{x+7}+\frac{3\left(x+5\right)}{x+7}$$

Since \frac{3x}{x+7} and \frac{3\left(x+5\right)}{x+7} have the same denominator, add them by adding their numerators.

$$\frac{3x+3\left(x+5\right)}{x+7}$$

Do the multiplications in 3x+3\left(x+5\right).

$$\frac{3x+3x+15}{x+7}$$

Combine like terms in 3x+3x+15.

$$\frac{6x+15}{x+7}$$