Solve 25^2-8*(15x-9+81x^2)/8x^3+5x^9-6-x

$${ 25 }^{ 2 } - \frac{ 8 \times (15x-9+81 { x }^{ 2 } ) }{ 8 { x }^{ 3 } +5 { x }^{ 9 } -6-x }$$

Evaluate

$$\frac{3125x^{9}+5000x^{3}-648x^{2}-745x-3678}{5x^{9}+8x^{3}-x-6}$$

Short Solution Steps

Calculate 25 to the power of 2 and get 625.

$$625-\frac{8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 625 times \frac{8x^{3}+5x^{9}-6-x}{8x^{3}+5x^{9}-6-x}.

$$\frac{625\left(8x^{3}+5x^{9}-6-x\right)}{8x^{3}+5x^{9}-6-x}-\frac{8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x}$$

Since \frac{625\left(8x^{3}+5x^{9}-6-x\right)}{8x^{3}+5x^{9}-6-x} and \frac{8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{625\left(8x^{3}+5x^{9}-6-x\right)-8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x}$$

Do the multiplications in 625\left(8x^{3}+5x^{9}-6-x\right)-8\left(15x-9+81x^{2}\right).

$$\frac{5000x^{3}+3125x^{9}-3750-625x-120x+72-648x^{2}}{8x^{3}+5x^{9}-6-x}$$

Combine like terms in 5000x^{3}+3125x^{9}-3750-625x-120x+72-648x^{2}.

$$\frac{5000x^{3}+3125x^{9}-3678-745x-648x^{2}}{8x^{3}+5x^{9}-6-x}$$

Expand

$$\frac{3125x^{9}+5000x^{3}-648x^{2}-745x-3678}{5x^{9}+8x^{3}-x-6}$$

Short Solution Steps

Calculate 25 to the power of 2 and get 625.

$$625-\frac{8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 625 times \frac{8x^{3}+5x^{9}-6-x}{8x^{3}+5x^{9}-6-x}.

$$\frac{625\left(8x^{3}+5x^{9}-6-x\right)}{8x^{3}+5x^{9}-6-x}-\frac{8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x}$$

Since \frac{625\left(8x^{3}+5x^{9}-6-x\right)}{8x^{3}+5x^{9}-6-x} and \frac{8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{625\left(8x^{3}+5x^{9}-6-x\right)-8\left(15x-9+81x^{2}\right)}{8x^{3}+5x^{9}-6-x}$$

Do the multiplications in 625\left(8x^{3}+5x^{9}-6-x\right)-8\left(15x-9+81x^{2}\right).

$$\frac{5000x^{3}+3125x^{9}-3750-625x-120x+72-648x^{2}}{8x^{3}+5x^{9}-6-x}$$

Combine like terms in 5000x^{3}+3125x^{9}-3750-625x-120x+72-648x^{2}.

$$\frac{5000x^{3}+3125x^{9}-3678-745x-648x^{2}}{8x^{3}+5x^{9}-6-x}$$