Solve 14-(x-3)(x^2-7x-30)/(x+2)(x^2+4x+3)/(x+3)(x-10)=

$$\frac { 14 - \frac { ( x - 3 ) ( x ^ { 2 } - 7 x - 30 ) } { ( x + 2 ) ( x ^ { 2 } + 4 x + 3 ) } } { ( x + 3 ) ( x - 10 ) } =$$

Evaluate

$$\frac{13x^{2}+55x-2}{\left(x-10\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}.

$$\frac{14-\frac{\left(x-10\right)\left(x-3\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}}{\left(x+3\right)\left(x-10\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{14-\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 14 times \frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}.

$$\frac{\frac{14\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}-\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Since \frac{14\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14\left(x+1\right)\left(x+2\right)-\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Do the multiplications in 14\left(x+1\right)\left(x+2\right)-\left(x-10\right)\left(x-3\right).

$$\frac{\frac{14x^{2}+28x+14x+28-x^{2}+3x+10x-30}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Combine like terms in 14x^{2}+28x+14x+28-x^{2}+3x+10x-30.

$$\frac{\frac{13x^{2}+55x-2}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Express \frac{\frac{13x^{2}+55x-2}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)} as a single fraction.

$$\frac{13x^{2}+55x-2}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x-10\right)}$$

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$\frac{13x^{2}+55x-2}{\left(x^{2}+3x+2\right)\left(x+3\right)\left(x-10\right)}$$

Use the distributive property to multiply x^{2}+3x+2 by x+3 and combine like terms.

$$\frac{13x^{2}+55x-2}{\left(x^{3}+6x^{2}+11x+6\right)\left(x-10\right)}$$

Use the distributive property to multiply x^{3}+6x^{2}+11x+6 by x-10 and combine like terms.

$$\frac{13x^{2}+55x-2}{x^{4}-4x^{3}-49x^{2}-104x-60}$$

Expand

$$\frac{13x^{2}+55x-2}{\left(x-10\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}.

$$\frac{14-\frac{\left(x-10\right)\left(x-3\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}}{\left(x+3\right)\left(x-10\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{14-\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 14 times \frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}.

$$\frac{\frac{14\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}-\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Since \frac{14\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14\left(x+1\right)\left(x+2\right)-\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Do the multiplications in 14\left(x+1\right)\left(x+2\right)-\left(x-10\right)\left(x-3\right).

$$\frac{\frac{14x^{2}+28x+14x+28-x^{2}+3x+10x-30}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Combine like terms in 14x^{2}+28x+14x+28-x^{2}+3x+10x-30.

$$\frac{\frac{13x^{2}+55x-2}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)}$$

Express \frac{\frac{13x^{2}+55x-2}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)} as a single fraction.

$$\frac{13x^{2}+55x-2}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x-10\right)}$$

Use the distributive property to multiply x+1 by x+2 and combine like terms.

$$\frac{13x^{2}+55x-2}{\left(x^{2}+3x+2\right)\left(x+3\right)\left(x-10\right)}$$

Use the distributive property to multiply x^{2}+3x+2 by x+3 and combine like terms.

$$\frac{13x^{2}+55x-2}{\left(x^{3}+6x^{2}+11x+6\right)\left(x-10\right)}$$

Use the distributive property to multiply x^{3}+6x^{2}+11x+6 by x-10 and combine like terms.

$$\frac{13x^{2}+55x-2}{x^{4}-4x^{3}-49x^{2}-104x-60}$$