# Solve for: (4x^2-4)/(x^7)/(x-1)/(x^4)

## Expression: $\frac{ 4{x}^{2}-4 }{ {x}^{7} }\div\frac{ x-1 }{ {x}^{4} }$

Factor out $4$ from the expression

$\frac{ 4\left( {x}^{2}-1 \right) }{ {x}^{7} }\div\frac{ x-1 }{ {x}^{4} }$

To divide by a fraction, multiply by the reciprocal of that fraction

$\frac{ 4\left( {x}^{2}-1 \right) }{ {x}^{7} } \times \frac{ {x}^{4} }{ x-1 }$

Use ${a}^{2}-{b}^{2}=\left( a-b \right)\left( a+b \right)$ to factor the expression

$\frac{ 4\left( x-1 \right) \times \left( x+1 \right) }{ {x}^{7} } \times \frac{ {x}^{4} }{ x-1 }$

Cancel out the common factor ${x}^{4}$

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

Cancel out the common factor $x-1$

$\frac{ 4\left( x+1 \right) }{ {x}^{3} }$

Distribute $4$ through the parentheses

$\frac{ 4x+4 }{ {x}^{3} }$

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