Solve f(x)=x^4/64*(x-4)^2/frac{x^2{4}-4}*1+x/1-x

$$f ( x ) = \frac { x ^ { 4 } } { 64 } \cdot \frac { ( x - 4 ) ^ { 2 } } { \frac { x ^ { 2 } } { 4 } - 4 } \cdot \frac { 1 + x } { 1 - x }$$

Evaluate

$$\frac{\left(x-4\right)\left(x+1\right)x^{4}}{16\left(1-x\right)\left(x+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{4}{4}.

$$\frac{x^{4}}{64}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}}{4}-\frac{4\times 4}{4}}\times \frac{1+x}{1-x}$$

Since \frac{x^{2}}{4} and \frac{4\times 4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{4}}{64}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-4\times 4}{4}}\times \frac{1+x}{1-x}$$

Do the multiplications in x^{2}-4\times 4.

$$\frac{x^{4}}{64}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}\times \frac{1+x}{1-x}$$

Multiply \frac{x^{4}}{64} times \frac{1+x}{1-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{4}\left(1+x\right)}{64\left(1-x\right)}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}$$

Use the distributive property to multiply x^{4} by 1+x.

$$\frac{x^{4}+x^{5}}{64\left(1-x\right)}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}$$

Use the distributive property to multiply 64 by 1-x.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}$$

Divide \left(x-4\right)^{2} by \frac{x^{2}-16}{4} by multiplying \left(x-4\right)^{2} by the reciprocal of \frac{x^{2}-16}{4}.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{\left(x-4\right)^{2}\times 4}{x^{2}-16}$$

Factor the expressions that are not already factored in \frac{\left(x-4\right)^{2}\times 4}{x^{2}-16}.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{4\left(x-4\right)^{2}}{\left(x-4\right)\left(x+4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{4\left(x-4\right)}{x+4}$$

Multiply \frac{x^{4}+x^{5}}{64-64x} times \frac{4\left(x-4\right)}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{4}+x^{5}\right)\times 4\left(x-4\right)}{\left(64-64x\right)\left(x+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(x-4\right)\left(x+1\right)x^{4}}{64\left(x+4\right)\left(-x+1\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+1\right)x^{4}}{16\left(x+4\right)\left(-x+1\right)}$$

Expand the expression.

$$\frac{x^{6}-3x^{5}-4x^{4}}{-16x^{2}-48x+64}$$

Expand

$$\frac{x^{6}-3x^{5}-4x^{4}}{16\left(1-x\right)\left(x+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{4}{4}.

$$\frac{x^{4}}{64}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}}{4}-\frac{4\times 4}{4}}\times \frac{1+x}{1-x}$$

Since \frac{x^{2}}{4} and \frac{4\times 4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{4}}{64}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-4\times 4}{4}}\times \frac{1+x}{1-x}$$

Do the multiplications in x^{2}-4\times 4.

$$\frac{x^{4}}{64}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}\times \frac{1+x}{1-x}$$

Multiply \frac{x^{4}}{64} times \frac{1+x}{1-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{4}\left(1+x\right)}{64\left(1-x\right)}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}$$

Use the distributive property to multiply x^{4} by 1+x.

$$\frac{x^{4}+x^{5}}{64\left(1-x\right)}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}$$

Use the distributive property to multiply 64 by 1-x.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{\left(x-4\right)^{2}}{\frac{x^{2}-16}{4}}$$

Divide \left(x-4\right)^{2} by \frac{x^{2}-16}{4} by multiplying \left(x-4\right)^{2} by the reciprocal of \frac{x^{2}-16}{4}.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{\left(x-4\right)^{2}\times 4}{x^{2}-16}$$

Factor the expressions that are not already factored in \frac{\left(x-4\right)^{2}\times 4}{x^{2}-16}.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{4\left(x-4\right)^{2}}{\left(x-4\right)\left(x+4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x^{4}+x^{5}}{64-64x}\times \frac{4\left(x-4\right)}{x+4}$$

Multiply \frac{x^{4}+x^{5}}{64-64x} times \frac{4\left(x-4\right)}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{4}+x^{5}\right)\times 4\left(x-4\right)}{\left(64-64x\right)\left(x+4\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(x-4\right)\left(x+1\right)x^{4}}{64\left(x+4\right)\left(-x+1\right)}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+1\right)x^{4}}{16\left(x+4\right)\left(-x+1\right)}$$

Expand the expression.

$$\frac{x^{6}-3x^{5}-4x^{4}}{-16x^{2}-48x+64}$$