Solve x^2-4/x^2+6x+9div((x^2+4x+4)divx^2-9)

$$\frac{ { x }^{ 2 } -4 }{ { x }^{ 2 } +6x+9 } \div (( { x }^{ 2 } +4x+4) \div { x }^{ 2 } -9)$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{x^{2}-4}{x^{2}+6x+9}}{\frac{x^{2}+4x+4}{x^{2}}-\frac{9x^{2}}{x^{2}}}$$

Since \frac{x^{2}+4x+4}{x^{2}} and \frac{9x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-4}{x^{2}+6x+9}}{\frac{x^{2}+4x+4-9x^{2}}{x^{2}}}$$

Combine like terms in x^{2}+4x+4-9x^{2}.

$$\frac{\frac{x^{2}-4}{x^{2}+6x+9}}{\frac{-8x^{2}+4x+4}{x^{2}}}$$

Divide \frac{x^{2}-4}{x^{2}+6x+9} by \frac{-8x^{2}+4x+4}{x^{2}} by multiplying \frac{x^{2}-4}{x^{2}+6x+9} by the reciprocal of \frac{-8x^{2}+4x+4}{x^{2}}.

$$\frac{\left(x^{2}-4\right)x^{2}}{\left(x^{2}+6x+9\right)\left(-8x^{2}+4x+4\right)}$$

Use the distributive property to multiply x^{2}-4 by x^{2}.

$$\frac{x^{4}-4x^{2}}{\left(x^{2}+6x+9\right)\left(-8x^{2}+4x+4\right)}$$

Use the distributive property to multiply x^{2}+6x+9 by -8x^{2}+4x+4 and combine like terms.

$$\frac{x^{4}-4x^{2}}{-8x^{4}-44x^{3}-44x^{2}+60x+36}$$

Expand

$$-\frac{x^{4}-4x^{2}}{4\left(2x^{2}-x-1\right)\left(x^{2}+6x+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{x^{2}-4}{x^{2}+6x+9}}{\frac{x^{2}+4x+4}{x^{2}}-\frac{9x^{2}}{x^{2}}}$$

Since \frac{x^{2}+4x+4}{x^{2}} and \frac{9x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-4}{x^{2}+6x+9}}{\frac{x^{2}+4x+4-9x^{2}}{x^{2}}}$$

Combine like terms in x^{2}+4x+4-9x^{2}.

$$\frac{\frac{x^{2}-4}{x^{2}+6x+9}}{\frac{-8x^{2}+4x+4}{x^{2}}}$$

Divide \frac{x^{2}-4}{x^{2}+6x+9} by \frac{-8x^{2}+4x+4}{x^{2}} by multiplying \frac{x^{2}-4}{x^{2}+6x+9} by the reciprocal of \frac{-8x^{2}+4x+4}{x^{2}}.

$$\frac{\left(x^{2}-4\right)x^{2}}{\left(x^{2}+6x+9\right)\left(-8x^{2}+4x+4\right)}$$

Use the distributive property to multiply x^{2}-4 by x^{2}.

$$\frac{x^{4}-4x^{2}}{\left(x^{2}+6x+9\right)\left(-8x^{2}+4x+4\right)}$$

Use the distributive property to multiply x^{2}+6x+9 by -8x^{2}+4x+4 and combine like terms.

$$\frac{x^{4}-4x^{2}}{-8x^{4}-44x^{3}-44x^{2}+60x+36}$$