Solve x^3-8/61xdivx^2x-2/16x^3

$$\frac { x ^ { 3 } - 8 } { 61 x } \div \frac { x ^ { 2 } x - 2 } { 16 x ^ { 3 } }$$

Evaluate

$$\frac{16x^{2}\left(x^{3}-8\right)}{61\left(x^{3}-2\right)}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\frac{x^{3}-8}{61x}}{\frac{x^{3}-2}{16x^{3}}}$$

Divide \frac{x^{3}-8}{61x} by \frac{x^{3}-2}{16x^{3}} by multiplying \frac{x^{3}-8}{61x} by the reciprocal of \frac{x^{3}-2}{16x^{3}}.

$$\frac{\left(x^{3}-8\right)\times 16x^{3}}{61x\left(x^{3}-2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{16x^{2}\left(x^{3}-8\right)}{61\left(x^{3}-2\right)}$$

Use the distributive property to multiply 16x^{2} by x^{3}-8.

$$\frac{16x^{5}-128x^{2}}{61\left(x^{3}-2\right)}$$

Use the distributive property to multiply 61 by x^{3}-2.

$$\frac{16x^{5}-128x^{2}}{61x^{3}-122}$$

Expand

$$\frac{16\left(x^{5}-8x^{2}\right)}{61\left(x^{3}-2\right)}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\frac{x^{3}-8}{61x}}{\frac{x^{3}-2}{16x^{3}}}$$

Divide \frac{x^{3}-8}{61x} by \frac{x^{3}-2}{16x^{3}} by multiplying \frac{x^{3}-8}{61x} by the reciprocal of \frac{x^{3}-2}{16x^{3}}.

$$\frac{\left(x^{3}-8\right)\times 16x^{3}}{61x\left(x^{3}-2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{16x^{2}\left(x^{3}-8\right)}{61\left(x^{3}-2\right)}$$

Use the distributive property to multiply 16x^{2} by x^{3}-8.

$$\frac{16x^{5}-128x^{2}}{61\left(x^{3}-2\right)}$$

Use the distributive property to multiply 61 by x^{3}-2.

$$\frac{16x^{5}-128x^{2}}{61x^{3}-122}$$