Solve 9x^2+x-15/4x^2-2x*6x^2+11x-10/x^2+6x+9

$$\frac { 9 x ^ { 2 } + x - 15 } { 4 x ^ { 2 } - 2 x } \times \frac { 6 x ^ { 2 } + 11 x - 10 } { x ^ { 2 } + 6 x + 9 }$$

Evaluate

$$\frac{\left(6x^{2}+11x-10\right)\left(9x^{2}+x-15\right)}{2x\left(2x-1\right)\left(x+3\right)^{2}}$$

Short Solution Steps

Multiply \frac{9x^{2}+x-15}{4x^{2}-2x} times \frac{6x^{2}+11x-10}{x^{2}+6x+9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9x^{2}+x-15\right)\left(6x^{2}+11x-10\right)}{\left(4x^{2}-2x\right)\left(x^{2}+6x+9\right)}$$

Use the distributive property to multiply 9x^{2}+x-15 by 6x^{2}+11x-10 and combine like terms.

$$\frac{54x^{4}+105x^{3}-169x^{2}-175x+150}{\left(4x^{2}-2x\right)\left(x^{2}+6x+9\right)}$$

Use the distributive property to multiply 4x^{2}-2x by x^{2}+6x+9 and combine like terms.

$$\frac{54x^{4}+105x^{3}-169x^{2}-175x+150}{4x^{4}+22x^{3}+24x^{2}-18x}$$

Expand

$$\frac{54x^{4}+105x^{3}-169x^{2}-175x+150}{2\left(2x^{2}-x\right)\left(x^{2}+6x+9\right)}$$

Short Solution Steps

Multiply \frac{9x^{2}+x-15}{4x^{2}-2x} times \frac{6x^{2}+11x-10}{x^{2}+6x+9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9x^{2}+x-15\right)\left(6x^{2}+11x-10\right)}{\left(4x^{2}-2x\right)\left(x^{2}+6x+9\right)}$$

Use the distributive property to multiply 9x^{2}+x-15 by 6x^{2}+11x-10 and combine like terms.

$$\frac{54x^{4}+105x^{3}-169x^{2}-175x+150}{\left(4x^{2}-2x\right)\left(x^{2}+6x+9\right)}$$

Use the distributive property to multiply 4x^{2}-2x by x^{2}+6x+9 and combine like terms.

$$\frac{54x^{4}+105x^{3}-169x^{2}-175x+150}{4x^{4}+22x^{3}+24x^{2}-18x}$$