Solve frac{4x^{2}-3x-10}{10x^{2}-33x+20}*(15x^2+19x-10/5x^2+28x-12div3x^2-x-10/5x^2+26x-24)

$$\frac { 4 x ^ { 2 } - 3 x - 10 } { 10 x ^ { 2 } - 33 x + 20 } \cdot ( \frac { 15 x ^ { 2 } + 19 x - 10 } { 5 x ^ { 2 } + 28 x - 12 } \div \frac { 3 x ^ { 2 } - x - 10 } { 5 x ^ { 2 } + 26 x - 24 } )$$

Evaluate

$$\frac{4x+5}{2x-5}$$

Short Solution Steps

Divide \frac{15x^{2}+19x-10}{5x^{2}+28x-12} by \frac{3x^{2}-x-10}{5x^{2}+26x-24} by multiplying \frac{15x^{2}+19x-10}{5x^{2}+28x-12} by the reciprocal of \frac{3x^{2}-x-10}{5x^{2}+26x-24}.

$$\frac{4x^{2}-3x-10}{10x^{2}-33x+20}\times \frac{\left(15x^{2}+19x-10\right)\left(5x^{2}+26x-24\right)}{\left(5x^{2}+28x-12\right)\left(3x^{2}-x-10\right)}$$

Factor the expressions that are not already factored in \frac{\left(15x^{2}+19x-10\right)\left(5x^{2}+26x-24\right)}{\left(5x^{2}+28x-12\right)\left(3x^{2}-x-10\right)}.

$$\frac{4x^{2}-3x-10}{10x^{2}-33x+20}\times \frac{\left(5x-4\right)\left(5x-2\right)\left(x+6\right)\left(3x+5\right)}{\left(x-2\right)\left(5x-2\right)\left(x+6\right)\left(3x+5\right)}$$

Cancel out \left(5x-2\right)\left(x+6\right)\left(3x+5\right) in both numerator and denominator.

$$\frac{4x^{2}-3x-10}{10x^{2}-33x+20}\times \frac{5x-4}{x-2}$$

Multiply \frac{4x^{2}-3x-10}{10x^{2}-33x+20} times \frac{5x-4}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}-3x-10\right)\left(5x-4\right)}{\left(10x^{2}-33x+20\right)\left(x-2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-2\right)\left(5x-4\right) in both numerator and denominator.

$$\frac{4x+5}{2x-5}$$

Expand

$$\frac{4x+5}{2x-5}$$

Short Solution Steps

Divide \frac{15x^{2}+19x-10}{5x^{2}+28x-12} by \frac{3x^{2}-x-10}{5x^{2}+26x-24} by multiplying \frac{15x^{2}+19x-10}{5x^{2}+28x-12} by the reciprocal of \frac{3x^{2}-x-10}{5x^{2}+26x-24}.

$$\frac{4x^{2}-3x-10}{10x^{2}-33x+20}\times \frac{\left(15x^{2}+19x-10\right)\left(5x^{2}+26x-24\right)}{\left(5x^{2}+28x-12\right)\left(3x^{2}-x-10\right)}$$

Factor the expressions that are not already factored in \frac{\left(15x^{2}+19x-10\right)\left(5x^{2}+26x-24\right)}{\left(5x^{2}+28x-12\right)\left(3x^{2}-x-10\right)}.

$$\frac{4x^{2}-3x-10}{10x^{2}-33x+20}\times \frac{\left(5x-4\right)\left(5x-2\right)\left(x+6\right)\left(3x+5\right)}{\left(x-2\right)\left(5x-2\right)\left(x+6\right)\left(3x+5\right)}$$

Cancel out \left(5x-2\right)\left(x+6\right)\left(3x+5\right) in both numerator and denominator.

$$\frac{4x^{2}-3x-10}{10x^{2}-33x+20}\times \frac{5x-4}{x-2}$$

Multiply \frac{4x^{2}-3x-10}{10x^{2}-33x+20} times \frac{5x-4}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}-3x-10\right)\left(5x-4\right)}{\left(10x^{2}-33x+20\right)\left(x-2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-2\right)\left(5x-4\right) in both numerator and denominator.

$$\frac{4x+5}{2x-5}$$