Solve (2x ^ 2 + 3x + 1)/(x + 5) / ((x ^ 2 - 1)/(x ^ 3 + 10x + 25)) = | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{2x^{2}+3x+1}{x+5}\div\frac{x^{2}-1}{x^{3}+10x+25}=$$

Evaluate

$\frac{\left(2x+1\right)\left(x^{3}+10x+25\right)}{\left(x-1\right)\left(x+5\right)}$

Short Solution Steps

Divide $\frac{2x^{2}+3x+1}{x+5}$ by $\frac{x^{2}-1}{x^{3}+10x+25}$ by multiplying $\frac{2x^{2}+3x+1}{x+5}$ by the reciprocal of $\frac{x^{2}-1}{x^{3}+10x+25}$.

$$\frac{\left(2x^{2}+3x+1\right)\left(x^{3}+10x+25\right)}{\left(x+5\right)\left(x^{2}-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(2x+1\right)\left(x^{3}+10x+25\right)}{\left(x-1\right)\left(x+1\right)\left(x+5\right)}$$

Cancel out $x+1$ in both numerator and denominator.

$$\frac{\left(2x+1\right)\left(x^{3}+10x+25\right)}{\left(x-1\right)\left(x+5\right)}$$

Expand the expression.

$$\frac{2x^{4}+x^{3}+20x^{2}+60x+25}{x^{2}+4x-5}$$

Expand

$\frac{2x^{4}+x^{3}+20x^{2}+60x+25}{\left(x-1\right)\left(x+5\right)}$

Short Solution Steps

Divide $\frac{2x^{2}+3x+1}{x+5}$ by $\frac{x^{2}-1}{x^{3}+10x+25}$ by multiplying $\frac{2x^{2}+3x+1}{x+5}$ by the reciprocal of $\frac{x^{2}-1}{x^{3}+10x+25}$.

$$\frac{\left(2x^{2}+3x+1\right)\left(x^{3}+10x+25\right)}{\left(x+5\right)\left(x^{2}-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(2x+1\right)\left(x^{3}+10x+25\right)}{\left(x-1\right)\left(x+1\right)\left(x+5\right)}$$

Cancel out $x+1$ in both numerator and denominator.

$$\frac{\left(2x+1\right)\left(x^{3}+10x+25\right)}{\left(x-1\right)\left(x+5\right)}$$

Expand the expression.

$$\frac{2x^{4}+x^{3}+20x^{2}+60x+25}{x^{2}+4x-5}$$