Solve (x+2/1-3)-7/frac{x+2{x-3}+6}

$$\frac { ( \frac { x + 2 } { 1 - 3 } ) - 7 } { \frac { x + 2 } { x - 3 } + 6 }$$

Evaluate

$$-\frac{\left(x-3\right)\left(x+16\right)}{2\left(7x-16\right)}$$

Short Solution Steps

Subtract 3 from 1 to get -2.

$$\frac{\frac{x+2}{-2}-7}{\frac{x+2}{x-3}+6}$$

Multiply both numerator and denominator by -1.

$$\frac{\frac{-x-2}{2}-7}{\frac{x+2}{x-3}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{2}{2}.

$$\frac{\frac{-x-2}{2}-\frac{7\times 2}{2}}{\frac{x+2}{x-3}+6}$$

Since \frac{-x-2}{2} and \frac{7\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-x-2-7\times 2}{2}}{\frac{x+2}{x-3}+6}$$

Do the multiplications in -x-2-7\times 2.

$$\frac{\frac{-x-2-14}{2}}{\frac{x+2}{x-3}+6}$$

Combine like terms in -x-2-14.

$$\frac{\frac{-x-16}{2}}{\frac{x+2}{x-3}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-3}{x-3}.

$$\frac{\frac{-x-16}{2}}{\frac{x+2}{x-3}+\frac{6\left(x-3\right)}{x-3}}$$

Since \frac{x+2}{x-3} and \frac{6\left(x-3\right)}{x-3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-x-16}{2}}{\frac{x+2+6\left(x-3\right)}{x-3}}$$

Do the multiplications in x+2+6\left(x-3\right).

$$\frac{\frac{-x-16}{2}}{\frac{x+2+6x-18}{x-3}}$$

Combine like terms in x+2+6x-18.

$$\frac{\frac{-x-16}{2}}{\frac{7x-16}{x-3}}$$

Divide \frac{-x-16}{2} by \frac{7x-16}{x-3} by multiplying \frac{-x-16}{2} by the reciprocal of \frac{7x-16}{x-3}.

$$\frac{\left(-x-16\right)\left(x-3\right)}{2\left(7x-16\right)}$$

Apply the distributive property by multiplying each term of -x-16 by each term of x-3.

$$\frac{-x^{2}+3x-16x+48}{2\left(7x-16\right)}$$

Combine 3x and -16x to get -13x.

$$\frac{-x^{2}-13x+48}{2\left(7x-16\right)}$$

Use the distributive property to multiply 2 by 7x-16.

$$\frac{-x^{2}-13x+48}{14x-32}$$

Expand

$$-\frac{x^{2}+13x-48}{2\left(7x-16\right)}$$

Short Solution Steps

Subtract 3 from 1 to get -2.

$$\frac{\frac{x+2}{-2}-7}{\frac{x+2}{x-3}+6}$$

Multiply both numerator and denominator by -1.

$$\frac{\frac{-x-2}{2}-7}{\frac{x+2}{x-3}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{2}{2}.

$$\frac{\frac{-x-2}{2}-\frac{7\times 2}{2}}{\frac{x+2}{x-3}+6}$$

Since \frac{-x-2}{2} and \frac{7\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-x-2-7\times 2}{2}}{\frac{x+2}{x-3}+6}$$

Do the multiplications in -x-2-7\times 2.

$$\frac{\frac{-x-2-14}{2}}{\frac{x+2}{x-3}+6}$$

Combine like terms in -x-2-14.

$$\frac{\frac{-x-16}{2}}{\frac{x+2}{x-3}+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{x-3}{x-3}.

$$\frac{\frac{-x-16}{2}}{\frac{x+2}{x-3}+\frac{6\left(x-3\right)}{x-3}}$$

Since \frac{x+2}{x-3} and \frac{6\left(x-3\right)}{x-3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-x-16}{2}}{\frac{x+2+6\left(x-3\right)}{x-3}}$$

Do the multiplications in x+2+6\left(x-3\right).

$$\frac{\frac{-x-16}{2}}{\frac{x+2+6x-18}{x-3}}$$

Combine like terms in x+2+6x-18.

$$\frac{\frac{-x-16}{2}}{\frac{7x-16}{x-3}}$$

Divide \frac{-x-16}{2} by \frac{7x-16}{x-3} by multiplying \frac{-x-16}{2} by the reciprocal of \frac{7x-16}{x-3}.

$$\frac{\left(-x-16\right)\left(x-3\right)}{2\left(7x-16\right)}$$

Apply the distributive property by multiplying each term of -x-16 by each term of x-3.

$$\frac{-x^{2}+3x-16x+48}{2\left(7x-16\right)}$$

Combine 3x and -16x to get -13x.

$$\frac{-x^{2}-13x+48}{2\left(7x-16\right)}$$

Use the distributive property to multiply 2 by 7x-16.

$$\frac{-x^{2}-13x+48}{14x-32}$$