Solve frac{(3x^{2}-x^2)(-2x)}{(8x^2-4x^2)(29x^3)}

$$\frac { ( 3 x ^ { 2 } - x ^ { 2 } ) ( - 2 x ) } { ( 8 x ^ { 2 } - 4 x ^ { 2 } ) ( 29 x ^ { 3 } ) }$$

Evaluate

$$-\frac{1}{29x^{2}}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{-2\left(-x^{2}+3x^{2}\right)}{29x^{2}\left(-4x^{2}+8x^{2}\right)}$$

Combine -x^{2} and 3x^{2} to get 2x^{2}.

$$\frac{-2\times 2x^{2}}{29x^{2}\left(-4x^{2}+8x^{2}\right)}$$

Multiply -2 and 2 to get -4.

$$\frac{-4x^{2}}{29x^{2}\left(-4x^{2}+8x^{2}\right)}$$

Combine -4x^{2} and 8x^{2} to get 4x^{2}.

$$\frac{-4x^{2}}{29x^{2}\times 4x^{2}}$$

Multiply 29 and 4 to get 116.

$$\frac{-4x^{2}}{116x^{2}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{-4x^{2}}{116x^{4}}$$

Cancel out 4x^{2} in both numerator and denominator.

$$\frac{-1}{29x^{2}}$$

Expand

$$-\frac{1}{29x^{2}}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{-2\left(-x^{2}+3x^{2}\right)}{29x^{2}\left(-4x^{2}+8x^{2}\right)}$$

Combine -x^{2} and 3x^{2} to get 2x^{2}.

$$\frac{-2\times 2x^{2}}{29x^{2}\left(-4x^{2}+8x^{2}\right)}$$

Multiply -2 and 2 to get -4.

$$\frac{-4x^{2}}{29x^{2}\left(-4x^{2}+8x^{2}\right)}$$

Combine -4x^{2} and 8x^{2} to get 4x^{2}.

$$\frac{-4x^{2}}{29x^{2}\times 4x^{2}}$$

Multiply 29 and 4 to get 116.

$$\frac{-4x^{2}}{116x^{2}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{-4x^{2}}{116x^{4}}$$

Cancel out 4x^{2} in both numerator and denominator.

$$\frac{-1}{29x^{2}}$$