Solve x^2/9+x/3+1/4

$$\frac { x ^ { 2 } } { 9 } + \frac { x } { 3 } + \frac { 1 } { 4 }$$

Evaluate

$$\frac{\left(2x+3\right)^{2}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{x}{3} times \frac{3}{3}.

$$\frac{x^{2}}{9}+\frac{3x}{9}+\frac{1}{4}$$

Since \frac{x^{2}}{9} and \frac{3x}{9} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+3x}{9}+\frac{1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 4 is 36. Multiply \frac{x^{2}+3x}{9} times \frac{4}{4}. Multiply \frac{1}{4} times \frac{9}{9}.

$$\frac{4\left(x^{2}+3x\right)}{36}+\frac{9}{36}$$

Since \frac{4\left(x^{2}+3x\right)}{36} and \frac{9}{36} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x^{2}+3x\right)+9}{36}$$

Do the multiplications in 4\left(x^{2}+3x\right)+9.

$$\frac{4x^{2}+12x+9}{36}$$

Factor

$$\frac{\left(2x+3\right)^{2}}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{4x^{2}+12x+9}{36}$$

Consider 4x^{2}+12x+9. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=2x and b=3.

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

Rewrite the complete factored expression.

$$\frac{\left(2x+3\right)^{2}}{36}$$