Solve left(x+1/3right)left(x+3/6right)

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

Evaluate

$$x^{2}+\frac{5x}{6}+\frac{1}{6}$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Apply the distributive property by multiplying each term of x+\frac{1}{3} by each term of x+\frac{1}{2}.

$$x^{2}+x\times \frac{1}{2}+\frac{1}{3}x+\frac{1}{3}\times \frac{1}{2}$$

Combine x\times \frac{1}{2} and \frac{1}{3}x to get \frac{5}{6}x.

$$x^{2}+\frac{5}{6}x+\frac{1}{3}\times \frac{1}{2}$$

Multiply \frac{1}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+\frac{5}{6}x+\frac{1\times 1}{3\times 2}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 2}.

$$x^{2}+\frac{5}{6}x+\frac{1}{6}$$

Expand

$$x^{2}+\frac{5x}{6}+\frac{1}{6}$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Apply the distributive property by multiplying each term of x+\frac{1}{3} by each term of x+\frac{1}{2}.

$$x^{2}+x\times \frac{1}{2}+\frac{1}{3}x+\frac{1}{3}\times \frac{1}{2}$$

Combine x\times \frac{1}{2} and \frac{1}{3}x to get \frac{5}{6}x.

$$x^{2}+\frac{5}{6}x+\frac{1}{3}\times \frac{1}{2}$$

Multiply \frac{1}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+\frac{5}{6}x+\frac{1\times 1}{3\times 2}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 2}.

$$x^{2}+\frac{5}{6}x+\frac{1}{6}$$