Solve frac{x^{2}-15x+56}{2x^3-28x^2+98x}*-3/64-x^2div1-x/x^2-8x+7

$$\frac { x ^ { 2 } - 15 x + 56 } { 2 x ^ { 3 } - 28 x ^ { 2 } + 98 x } \cdot \frac { - 3 } { 64 - x ^ { 2 } } \div \frac { 1 - x } { x ^ { 2 } - 8 x + 7 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-15x+56}{2x^{3}-28x^{2}+98x}.

$$\frac{\frac{\left(x-8\right)\left(x-7\right)}{2x\left(x-7\right)^{2}}\times \frac{-3}{64-x^{2}}}{\frac{1-x}{x^{2}-8x+7}}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{\frac{x-8}{2x\left(x-7\right)}\times \frac{-3}{64-x^{2}}}{\frac{1-x}{x^{2}-8x+7}}$$

Multiply \frac{x-8}{2x\left(x-7\right)} times \frac{-3}{64-x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{1-x}{x^{2}-8x+7}}$$

Factor the expressions that are not already factored in \frac{1-x}{x^{2}-8x+7}.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{-x+1}{\left(x-7\right)\left(x-1\right)}}$$

Extract the negative sign in 1-x.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{-\left(x-1\right)}{\left(x-7\right)\left(x-1\right)}}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{-1}{x-7}}$$

Divide \frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)} by \frac{-1}{x-7} by multiplying \frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)} by the reciprocal of \frac{-1}{x-7}.

$$\frac{\left(x-8\right)\left(-3\right)\left(x-7\right)}{2x\left(x-7\right)\left(64-x^{2}\right)\left(-1\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{-3\left(x-8\right)}{-2x\left(-x^{2}+64\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-8 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-15x+56}{2x^{3}-28x^{2}+98x}.

$$\frac{\frac{\left(x-8\right)\left(x-7\right)}{2x\left(x-7\right)^{2}}\times \frac{-3}{64-x^{2}}}{\frac{1-x}{x^{2}-8x+7}}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{\frac{x-8}{2x\left(x-7\right)}\times \frac{-3}{64-x^{2}}}{\frac{1-x}{x^{2}-8x+7}}$$

Multiply \frac{x-8}{2x\left(x-7\right)} times \frac{-3}{64-x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{1-x}{x^{2}-8x+7}}$$

Factor the expressions that are not already factored in \frac{1-x}{x^{2}-8x+7}.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{-x+1}{\left(x-7\right)\left(x-1\right)}}$$

Extract the negative sign in 1-x.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{-\left(x-1\right)}{\left(x-7\right)\left(x-1\right)}}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{\frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)}}{\frac{-1}{x-7}}$$

Divide \frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)} by \frac{-1}{x-7} by multiplying \frac{\left(x-8\right)\left(-3\right)}{2x\left(x-7\right)\left(64-x^{2}\right)} by the reciprocal of \frac{-1}{x-7}.

$$\frac{\left(x-8\right)\left(-3\right)\left(x-7\right)}{2x\left(x-7\right)\left(64-x^{2}\right)\left(-1\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{-3\left(x-8\right)}{-2x\left(-x^{2}+64\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-8 in both numerator and denominator.

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

Expand the expression.

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