Solve frac{x^{4}-27x}{+7x-30}*x^2+20x+100/x^3+3x^2+9xdivx^2-10/x-3

$$\frac { x ^ { 4 } - 27 x } { + 7 x - 30 } \cdot \frac { x ^ { 2 } + 20 x + 100 } { x ^ { 3 } + 3 x ^ { 2 } + 9 x } \div \frac { x ^ { 2 } - 10 } { x - 3 }$$

Evaluate

$$\frac{\left(\left(x-3\right)\left(x+10\right)\right)^{2}}{\left(7x-30\right)\left(x^{2}-10\right)}$$

Short Solution Steps

Multiply \frac{x^{4}-27x}{7x-30} times \frac{x^{2}+20x+100}{x^{3}+3x^{2}+9x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)}}{\frac{x^{2}-10}{x-3}}$$

Divide \frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)} by \frac{x^{2}-10}{x-3} by multiplying \frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)} by the reciprocal of \frac{x^{2}-10}{x-3}.

$$\frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)\left(x-3\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)\left(x^{2}-10\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-3\right)^{2}\left(x+10\right)^{2}\left(x^{2}+3x+9\right)}{x\left(7x-30\right)\left(x^{2}-10\right)\left(x^{2}+3x+9\right)}$$

Cancel out x\left(x^{2}+3x+9\right) in both numerator and denominator.

$$\frac{\left(x-3\right)^{2}\left(x+10\right)^{2}}{\left(7x-30\right)\left(x^{2}-10\right)}$$

Expand the expression.

$$\frac{x^{4}+14x^{3}-11x^{2}-420x+900}{7x^{3}-30x^{2}-70x+300}$$

Expand

$$\frac{x^{4}+14x^{3}-11x^{2}-420x+900}{\left(7x-30\right)\left(x^{2}-10\right)}$$

Short Solution Steps

Multiply \frac{x^{4}-27x}{7x-30} times \frac{x^{2}+20x+100}{x^{3}+3x^{2}+9x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)}}{\frac{x^{2}-10}{x-3}}$$

Divide \frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)} by \frac{x^{2}-10}{x-3} by multiplying \frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)} by the reciprocal of \frac{x^{2}-10}{x-3}.

$$\frac{\left(x^{4}-27x\right)\left(x^{2}+20x+100\right)\left(x-3\right)}{\left(7x-30\right)\left(x^{3}+3x^{2}+9x\right)\left(x^{2}-10\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-3\right)^{2}\left(x+10\right)^{2}\left(x^{2}+3x+9\right)}{x\left(7x-30\right)\left(x^{2}-10\right)\left(x^{2}+3x+9\right)}$$

Cancel out x\left(x^{2}+3x+9\right) in both numerator and denominator.

$$\frac{\left(x-3\right)^{2}\left(x+10\right)^{2}}{\left(7x-30\right)\left(x^{2}-10\right)}$$

Expand the expression.

$$\frac{x^{4}+14x^{3}-11x^{2}-420x+900}{7x^{3}-30x^{2}-70x+300}$$