Solve 14x^3+3x^2/x^2-1+3x+1

$$14 \frac { x ^ { 3 } + 3 x ^ { 2 } } { x ^ { 2 } - 1 } + 3 x + 1$$

Evaluate

$$\frac{17x^{3}+43x^{2}-3x-1}{x^{2}-1}$$

Short Solution Steps

Express 14\times \frac{x^{3}+3x^{2}}{x^{2}-1} as a single fraction.

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

Factor x^{2}-1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x+1 times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.

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

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

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

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

$$\frac{14x^{3}+42x^{2}+3x^{3}-3x+x^{2}-1}{\left(x-1\right)\left(x+1\right)}$$

Combine like terms in 14x^{3}+42x^{2}+3x^{3}-3x+x^{2}-1.

$$\frac{17x^{3}+43x^{2}-3x-1}{\left(x-1\right)\left(x+1\right)}$$

Expand \left(x-1\right)\left(x+1\right).

$$\frac{17x^{3}+43x^{2}-3x-1}{x^{2}-1}$$

Expand

$$\frac{17x^{3}+43x^{2}-3x-1}{x^{2}-1}$$

Short Solution Steps

Express 14\times \frac{x^{3}+3x^{2}}{x^{2}-1} as a single fraction.

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

Factor x^{2}-1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x+1 times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.

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

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

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

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

$$\frac{14x^{3}+42x^{2}+3x^{3}-3x+x^{2}-1}{\left(x-1\right)\left(x+1\right)}$$

Combine like terms in 14x^{3}+42x^{2}+3x^{3}-3x+x^{2}-1.

$$\frac{17x^{3}+43x^{2}-3x-1}{\left(x-1\right)\left(x+1\right)}$$

Expand \left(x-1\right)\left(x+1\right).

$$\frac{17x^{3}+43x^{2}-3x-1}{x^{2}-1}$$