Solve 4x/x+3-4x^2-7/x^2+3x

$$\frac { 4 x } { x + 3 } - \frac { 4 x ^ { 2 } - 7 } { x ^ { 2 } + 3 x }$$

Evaluate

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

Short Solution Steps

Factor x^{2}+3x.

$$\frac{4x}{x+3}-\frac{4x^{2}-7}{x\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x\left(x+3\right) is x\left(x+3\right). Multiply \frac{4x}{x+3} times \frac{x}{x}.

$$\frac{4xx}{x\left(x+3\right)}-\frac{4x^{2}-7}{x\left(x+3\right)}$$

Since \frac{4xx}{x\left(x+3\right)} and \frac{4x^{2}-7}{x\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4xx-\left(4x^{2}-7\right)}{x\left(x+3\right)}$$

Do the multiplications in 4xx-\left(4x^{2}-7\right).

$$\frac{4x^{2}-4x^{2}+7}{x\left(x+3\right)}$$

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

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

Expand x\left(x+3\right).

$$\frac{7}{x^{2}+3x}$$

Expand

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

Short Solution Steps

Factor x^{2}+3x.

$$\frac{4x}{x+3}-\frac{4x^{2}-7}{x\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x\left(x+3\right) is x\left(x+3\right). Multiply \frac{4x}{x+3} times \frac{x}{x}.

$$\frac{4xx}{x\left(x+3\right)}-\frac{4x^{2}-7}{x\left(x+3\right)}$$

Since \frac{4xx}{x\left(x+3\right)} and \frac{4x^{2}-7}{x\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4xx-\left(4x^{2}-7\right)}{x\left(x+3\right)}$$

Do the multiplications in 4xx-\left(4x^{2}-7\right).

$$\frac{4x^{2}-4x^{2}+7}{x\left(x+3\right)}$$

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

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

Expand x\left(x+3\right).

$$\frac{7}{x^{2}+3x}$$