Solve (1+x):(3+x)(6+x)81

$$( 1 + x ) : ( 3 + x ) ( 6 + x ) 81$$

Evaluate

$$\frac{81\left(x+1\right)\left(x+6\right)}{x+3}$$

Short Solution Steps

Express \frac{1+x}{3+x}\left(6+x\right) as a single fraction.

$$\frac{\left(1+x\right)\left(6+x\right)}{3+x}\times 81$$

Express \frac{\left(1+x\right)\left(6+x\right)}{3+x}\times 81 as a single fraction.

$$\frac{\left(1+x\right)\left(6+x\right)\times 81}{3+x}$$

Apply the distributive property by multiplying each term of 1+x by each term of 6+x.

$$\frac{\left(6+x+6x+x^{2}\right)\times 81}{3+x}$$

Combine x and 6x to get 7x.

$$\frac{\left(6+7x+x^{2}\right)\times 81}{3+x}$$

Use the distributive property to multiply 6+7x+x^{2} by 81.

$$\frac{486+567x+81x^{2}}{3+x}$$

Expand

$$\frac{81\left(x^{2}+7x+6\right)}{x+3}$$

Short Solution Steps

Express \frac{1+x}{3+x}\left(6+x\right) as a single fraction.

$$\frac{\left(1+x\right)\left(6+x\right)}{3+x}\times 81$$

Express \frac{\left(1+x\right)\left(6+x\right)}{3+x}\times 81 as a single fraction.

$$\frac{\left(1+x\right)\left(6+x\right)\times 81}{3+x}$$

Apply the distributive property by multiplying each term of 1+x by each term of 6+x.

$$\frac{\left(6+x+6x+x^{2}\right)\times 81}{3+x}$$

Combine x and 6x to get 7x.

$$\frac{\left(6+7x+x^{2}\right)\times 81}{3+x}$$

Use the distributive property to multiply 6+7x+x^{2} by 81.

$$\frac{486+567x+81x^{2}}{3+x}$$