Solve (3+x)(-1)-(1-x)(1)divleft(3+xright)^2

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

Evaluate

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

Short Solution Steps

Use the distributive property to multiply 3+x by -1.

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

Use the distributive property to multiply 1-x by 1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -3-x times \frac{\left(3+x\right)^{2}}{\left(3+x\right)^{2}}.

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

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

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

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

$$\frac{-27-18x-3x^{2}-9x-6x^{2}-x^{3}-1+x}{\left(3+x\right)^{2}}$$

Combine like terms in -27-18x-3x^{2}-9x-6x^{2}-x^{3}-1+x.

$$\frac{-28-26x-9x^{2}-x^{3}}{\left(3+x\right)^{2}}$$

Expand \left(3+x\right)^{2}.

$$\frac{-28-26x-9x^{2}-x^{3}}{x^{2}+6x+9}$$

Expand

$$-\frac{x^{3}+9x^{2}+26x+28}{\left(x+3\right)^{2}}$$

Short Solution Steps

Use the distributive property to multiply 3+x by -1.

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

Use the distributive property to multiply 1-x by 1.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -3-x times \frac{\left(3+x\right)^{2}}{\left(3+x\right)^{2}}.

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

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

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

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

$$\frac{-27-18x-3x^{2}-9x-6x^{2}-x^{3}-1+x}{\left(3+x\right)^{2}}$$

Combine like terms in -27-18x-3x^{2}-9x-6x^{2}-x^{3}-1+x.

$$\frac{-28-26x-9x^{2}-x^{3}}{\left(3+x\right)^{2}}$$

Expand \left(3+x\right)^{2}.

$$\frac{-28-26x-9x^{2}-x^{3}}{x^{2}+6x+9}$$