Solve -8x+3/7x^2/frac{x^2-3x{x+2}}

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

Evaluate

$$-\frac{\left(x+2\right)\left(8x+3\right)}{7\left(x-3\right)x^{3}}$$

Short Solution Steps

Divide -\frac{8x+3}{7x^{2}} by \frac{x^{2}-3x}{x+2} by multiplying -\frac{8x+3}{7x^{2}} by the reciprocal of \frac{x^{2}-3x}{x+2}.

$$\frac{\left(-\frac{8x+3}{7x^{2}}\right)\left(x+2\right)}{x^{2}-3x}$$

Express \left(-\frac{8x+3}{7x^{2}}\right)\left(x+2\right) as a single fraction.

$$\frac{\frac{-\left(8x+3\right)\left(x+2\right)}{7x^{2}}}{x^{2}-3x}$$

Express \frac{\frac{-\left(8x+3\right)\left(x+2\right)}{7x^{2}}}{x^{2}-3x} as a single fraction.

$$\frac{-\left(8x+3\right)\left(x+2\right)}{7x^{2}\left(x^{2}-3x\right)}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\left(8x+3\right)\left(x+2\right)}{-7x^{2}\left(x^{2}-3x\right)}$$

Use the distributive property to multiply 8x+3 by x+2 and combine like terms.

$$\frac{8x^{2}+19x+6}{-7x^{2}\left(x^{2}-3x\right)}$$

Use the distributive property to multiply -7x^{2} by x^{2}-3x.

$$\frac{8x^{2}+19x+6}{-7x^{4}+21x^{3}}$$

Expand

$$-\frac{8x^{2}+19x+6}{7x^{2}\left(x^{2}-3x\right)}$$

Short Solution Steps

Divide -\frac{8x+3}{7x^{2}} by \frac{x^{2}-3x}{x+2} by multiplying -\frac{8x+3}{7x^{2}} by the reciprocal of \frac{x^{2}-3x}{x+2}.

$$\frac{\left(-\frac{8x+3}{7x^{2}}\right)\left(x+2\right)}{x^{2}-3x}$$

Express \left(-\frac{8x+3}{7x^{2}}\right)\left(x+2\right) as a single fraction.

$$\frac{\frac{-\left(8x+3\right)\left(x+2\right)}{7x^{2}}}{x^{2}-3x}$$

Express \frac{\frac{-\left(8x+3\right)\left(x+2\right)}{7x^{2}}}{x^{2}-3x} as a single fraction.

$$\frac{-\left(8x+3\right)\left(x+2\right)}{7x^{2}\left(x^{2}-3x\right)}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\left(8x+3\right)\left(x+2\right)}{-7x^{2}\left(x^{2}-3x\right)}$$

Use the distributive property to multiply 8x+3 by x+2 and combine like terms.

$$\frac{8x^{2}+19x+6}{-7x^{2}\left(x^{2}-3x\right)}$$

Use the distributive property to multiply -7x^{2} by x^{2}-3x.

$$\frac{8x^{2}+19x+6}{-7x^{4}+21x^{3}}$$