Solve 3x^2+78/5-x*2x^3-250/3x^2-1242

$$\frac { 3 x ^ { 2 } + 78 } { 5 - x } \cdot \frac { 2 x ^ { 3 } - 250 } { 3 x ^ { 2 } - 1242 }$$

Evaluate

$$-\frac{2\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{x^{2}-414}$$

Short Solution Steps

Multiply \frac{3x^{2}+78}{5-x} times \frac{2x^{3}-250}{3x^{2}-1242} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x^{2}+78\right)\left(2x^{3}-250\right)}{\left(5-x\right)\left(3x^{2}-1242\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 3\left(x-5\right)\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{3\left(-x+5\right)\left(x^{2}-414\right)}$$

Extract the negative sign in -5+x.

$$\frac{-2\times 3\left(-x+5\right)\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{3\left(-x+5\right)\left(x^{2}-414\right)}$$

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

$$\frac{-2\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{x^{2}-414}$$

Expand the expression.

$$\frac{-2x^{4}-10x^{3}-102x^{2}-260x-1300}{x^{2}-414}$$

Expand

$$-\frac{2\left(x^{4}+5x^{3}+51x^{2}+130x+650\right)}{x^{2}-414}$$

Short Solution Steps

Multiply \frac{3x^{2}+78}{5-x} times \frac{2x^{3}-250}{3x^{2}-1242} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x^{2}+78\right)\left(2x^{3}-250\right)}{\left(5-x\right)\left(3x^{2}-1242\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 3\left(x-5\right)\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{3\left(-x+5\right)\left(x^{2}-414\right)}$$

Extract the negative sign in -5+x.

$$\frac{-2\times 3\left(-x+5\right)\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{3\left(-x+5\right)\left(x^{2}-414\right)}$$

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

$$\frac{-2\left(x^{2}+26\right)\left(x^{2}+5x+25\right)}{x^{2}-414}$$

Expand the expression.

$$\frac{-2x^{4}-10x^{3}-102x^{2}-260x-1300}{x^{2}-414}$$