Solve 2x-1/x^2+10x+25+7x/4x+20

$$\frac { 2 x - 1 } { x ^ { 2 } + 10 x + 25 } + \frac { 7 x } { 4 x + 20 }$$

Evaluate

$$\frac{7x^{2}+43x-4}{4\left(x+5\right)^{2}}$$

Short Solution Steps

Factor x^{2}+10x+25. Factor 4x+20.

$$\frac{2x-1}{\left(x+5\right)^{2}}+\frac{7x}{4\left(x+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+5\right)^{2} and 4\left(x+5\right) is 4\left(x+5\right)^{2}. Multiply \frac{2x-1}{\left(x+5\right)^{2}} times \frac{4}{4}. Multiply \frac{7x}{4\left(x+5\right)} times \frac{x+5}{x+5}.

$$\frac{4\left(2x-1\right)}{4\left(x+5\right)^{2}}+\frac{7x\left(x+5\right)}{4\left(x+5\right)^{2}}$$

Since \frac{4\left(2x-1\right)}{4\left(x+5\right)^{2}} and \frac{7x\left(x+5\right)}{4\left(x+5\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4\left(2x-1\right)+7x\left(x+5\right)}{4\left(x+5\right)^{2}}$$

Do the multiplications in 4\left(2x-1\right)+7x\left(x+5\right).

$$\frac{8x-4+7x^{2}+35x}{4\left(x+5\right)^{2}}$$

Combine like terms in 8x-4+7x^{2}+35x.

$$\frac{43x-4+7x^{2}}{4\left(x+5\right)^{2}}$$

Expand 4\left(x+5\right)^{2}.

$$\frac{43x-4+7x^{2}}{4x^{2}+40x+100}$$

Expand

$$\frac{7x^{2}+43x-4}{4\left(x+5\right)^{2}}$$

Short Solution Steps

Factor x^{2}+10x+25. Factor 4x+20.

$$\frac{2x-1}{\left(x+5\right)^{2}}+\frac{7x}{4\left(x+5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+5\right)^{2} and 4\left(x+5\right) is 4\left(x+5\right)^{2}. Multiply \frac{2x-1}{\left(x+5\right)^{2}} times \frac{4}{4}. Multiply \frac{7x}{4\left(x+5\right)} times \frac{x+5}{x+5}.

$$\frac{4\left(2x-1\right)}{4\left(x+5\right)^{2}}+\frac{7x\left(x+5\right)}{4\left(x+5\right)^{2}}$$

Since \frac{4\left(2x-1\right)}{4\left(x+5\right)^{2}} and \frac{7x\left(x+5\right)}{4\left(x+5\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4\left(2x-1\right)+7x\left(x+5\right)}{4\left(x+5\right)^{2}}$$

Do the multiplications in 4\left(2x-1\right)+7x\left(x+5\right).

$$\frac{8x-4+7x^{2}+35x}{4\left(x+5\right)^{2}}$$

Combine like terms in 8x-4+7x^{2}+35x.

$$\frac{43x-4+7x^{2}}{4\left(x+5\right)^{2}}$$

Expand 4\left(x+5\right)^{2}.

$$\frac{43x-4+7x^{2}}{4x^{2}+40x+100}$$