Solve (5x^2-4x-1/2x^2+x-3)(8x^2+27/2x-1)

$$( \frac { 5 x ^ { 2 } - 4 x - 1 } { 2 x ^ { 2 } + x - 3 } ) ( \frac { 8 x ^ { 2 } + 27 } { 2 x - 1 } )$$

Evaluate

$$\frac{\left(5x+1\right)\left(8x^{2}+27\right)}{\left(2x-1\right)\left(2x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5x^{2}-4x-1}{2x^{2}+x-3}.

$$\frac{\left(x-1\right)\left(5x+1\right)}{\left(x-1\right)\left(2x+3\right)}\times \frac{8x^{2}+27}{2x-1}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{5x+1}{2x+3}\times \frac{8x^{2}+27}{2x-1}$$

Multiply \frac{5x+1}{2x+3} times \frac{8x^{2}+27}{2x-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5x+1\right)\left(8x^{2}+27\right)}{\left(2x+3\right)\left(2x-1\right)}$$

Use the distributive property to multiply 5x+1 by 8x^{2}+27.

$$\frac{40x^{3}+135x+8x^{2}+27}{\left(2x+3\right)\left(2x-1\right)}$$

Use the distributive property to multiply 2x+3 by 2x-1 and combine like terms.

$$\frac{40x^{3}+135x+8x^{2}+27}{4x^{2}+4x-3}$$

Expand

$$\frac{40x^{3}+8x^{2}+135x+27}{\left(2x-1\right)\left(2x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5x^{2}-4x-1}{2x^{2}+x-3}.

$$\frac{\left(x-1\right)\left(5x+1\right)}{\left(x-1\right)\left(2x+3\right)}\times \frac{8x^{2}+27}{2x-1}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{5x+1}{2x+3}\times \frac{8x^{2}+27}{2x-1}$$

Multiply \frac{5x+1}{2x+3} times \frac{8x^{2}+27}{2x-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5x+1\right)\left(8x^{2}+27\right)}{\left(2x+3\right)\left(2x-1\right)}$$

Use the distributive property to multiply 5x+1 by 8x^{2}+27.

$$\frac{40x^{3}+135x+8x^{2}+27}{\left(2x+3\right)\left(2x-1\right)}$$

Use the distributive property to multiply 2x+3 by 2x-1 and combine like terms.

$$\frac{40x^{3}+135x+8x^{2}+27}{4x^{2}+4x-3}$$