Solve 13x^4+7x^6+25x-1/-3x+x+7+6x^5+5x

$$\frac { 13 x ^ { 4 } + 7 x ^ { 6 } + 25 x - 1 } { - 3 x + x + 7 } + 6 x ^ { 5 } + 5 x$$

Evaluate

$$\frac{-5x^{6}+42x^{5}+13x^{4}-10x^{2}+60x-1}{7-2x}$$

Short Solution Steps

Combine -3x and x to get -2x.

$$\frac{13x^{4}+7x^{6}+25x-1}{-2x+7}+6x^{5}+5x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{5}+5x times \frac{-2x+7}{-2x+7}.

$$\frac{13x^{4}+7x^{6}+25x-1}{-2x+7}+\frac{\left(6x^{5}+5x\right)\left(-2x+7\right)}{-2x+7}$$

Since \frac{13x^{4}+7x^{6}+25x-1}{-2x+7} and \frac{\left(6x^{5}+5x\right)\left(-2x+7\right)}{-2x+7} have the same denominator, add them by adding their numerators.

$$\frac{13x^{4}+7x^{6}+25x-1+\left(6x^{5}+5x\right)\left(-2x+7\right)}{-2x+7}$$

Do the multiplications in 13x^{4}+7x^{6}+25x-1+\left(6x^{5}+5x\right)\left(-2x+7\right).

$$\frac{13x^{4}+7x^{6}+25x-1-12x^{6}+42x^{5}-10x^{2}+35x}{-2x+7}$$

Combine like terms in 13x^{4}+7x^{6}+25x-1-12x^{6}+42x^{5}-10x^{2}+35x.

$$\frac{13x^{4}+60x-5x^{6}-1+42x^{5}-10x^{2}}{-2x+7}$$

Expand

$$\frac{-5x^{6}+42x^{5}+13x^{4}-10x^{2}+60x-1}{7-2x}$$

Short Solution Steps

Combine -3x and x to get -2x.

$$\frac{13x^{4}+7x^{6}+25x-1}{-2x+7}+6x^{5}+5x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{5}+5x times \frac{-2x+7}{-2x+7}.

$$\frac{13x^{4}+7x^{6}+25x-1}{-2x+7}+\frac{\left(6x^{5}+5x\right)\left(-2x+7\right)}{-2x+7}$$

Since \frac{13x^{4}+7x^{6}+25x-1}{-2x+7} and \frac{\left(6x^{5}+5x\right)\left(-2x+7\right)}{-2x+7} have the same denominator, add them by adding their numerators.

$$\frac{13x^{4}+7x^{6}+25x-1+\left(6x^{5}+5x\right)\left(-2x+7\right)}{-2x+7}$$

Do the multiplications in 13x^{4}+7x^{6}+25x-1+\left(6x^{5}+5x\right)\left(-2x+7\right).

$$\frac{13x^{4}+7x^{6}+25x-1-12x^{6}+42x^{5}-10x^{2}+35x}{-2x+7}$$

Combine like terms in 13x^{4}+7x^{6}+25x-1-12x^{6}+42x^{5}-10x^{2}+35x.

$$\frac{13x^{4}+60x-5x^{6}-1+42x^{5}-10x^{2}}{-2x+7}$$