Solve g(x)=15-x/frac{1{x-7}-1/8}

$$g ( x ) = \frac { 15 - x } { \frac { 1 } { x - 7 } - \frac { 1 } { 8 } }$$

Evaluate

$$8\left(x-7\right)$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-7 and 8 is 8\left(x-7\right). Multiply \frac{1}{x-7} times \frac{8}{8}. Multiply \frac{1}{8} times \frac{x-7}{x-7}.

$$\frac{15-x}{\frac{8}{8\left(x-7\right)}-\frac{x-7}{8\left(x-7\right)}}$$

Since \frac{8}{8\left(x-7\right)} and \frac{x-7}{8\left(x-7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-x}{\frac{8-\left(x-7\right)}{8\left(x-7\right)}}$$

Do the multiplications in 8-\left(x-7\right).

$$\frac{15-x}{\frac{8-x+7}{8\left(x-7\right)}}$$

Combine like terms in 8-x+7.

$$\frac{15-x}{\frac{15-x}{8\left(x-7\right)}}$$

Divide 15-x by \frac{15-x}{8\left(x-7\right)} by multiplying 15-x by the reciprocal of \frac{15-x}{8\left(x-7\right)}.

$$\frac{\left(15-x\right)\times 8\left(x-7\right)}{15-x}$$

Cancel out -x+15 in both numerator and denominator.

$$8\left(x-7\right)$$

Use the distributive property to multiply 8 by x-7.

$$8x-56$$

Expand

$$8x-56$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-7 and 8 is 8\left(x-7\right). Multiply \frac{1}{x-7} times \frac{8}{8}. Multiply \frac{1}{8} times \frac{x-7}{x-7}.

$$\frac{15-x}{\frac{8}{8\left(x-7\right)}-\frac{x-7}{8\left(x-7\right)}}$$

Since \frac{8}{8\left(x-7\right)} and \frac{x-7}{8\left(x-7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-x}{\frac{8-\left(x-7\right)}{8\left(x-7\right)}}$$

Do the multiplications in 8-\left(x-7\right).

$$\frac{15-x}{\frac{8-x+7}{8\left(x-7\right)}}$$

Combine like terms in 8-x+7.

$$\frac{15-x}{\frac{15-x}{8\left(x-7\right)}}$$

Divide 15-x by \frac{15-x}{8\left(x-7\right)} by multiplying 15-x by the reciprocal of \frac{15-x}{8\left(x-7\right)}.

$$\frac{\left(15-x\right)\times 8\left(x-7\right)}{15-x}$$

Cancel out -x+15 in both numerator and denominator.

$$8\left(x-7\right)$$

Use the distributive property to multiply 8 by x-7.

$$8x-56$$