Solve (x-3)^2/2^2+(x+1)^2/3^2

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

Evaluate

$$\frac{13x^{2}}{36}-\frac{23x}{18}+\frac{85}{36}$$

Short Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(x-3\right)^{2}}{4}+\frac{\left(x+1\right)^{2}}{9}$$

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

$$\frac{9\left(x-3\right)^{2}}{36}+\frac{4\left(x+1\right)^{2}}{36}$$

Since \frac{9\left(x-3\right)^{2}}{36} and \frac{4\left(x+1\right)^{2}}{36} have the same denominator, add them by adding their numerators.

$$\frac{9\left(x-3\right)^{2}+4\left(x+1\right)^{2}}{36}$$

Do the multiplications in 9\left(x-3\right)^{2}+4\left(x+1\right)^{2}.

$$\frac{9x^{2}-54x+81+4x^{2}+8x+4}{36}$$

Combine like terms in 9x^{2}-54x+81+4x^{2}+8x+4.

$$\frac{13x^{2}-46x+85}{36}$$

Expand

$$\frac{13x^{2}}{36}-\frac{23x}{18}+\frac{85}{36}$$

Short Solution Steps

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(x-3\right)^{2}}{4}+\frac{\left(x+1\right)^{2}}{9}$$

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

$$\frac{9\left(x-3\right)^{2}}{36}+\frac{4\left(x+1\right)^{2}}{36}$$

Since \frac{9\left(x-3\right)^{2}}{36} and \frac{4\left(x+1\right)^{2}}{36} have the same denominator, add them by adding their numerators.

$$\frac{9\left(x-3\right)^{2}+4\left(x+1\right)^{2}}{36}$$

Do the multiplications in 9\left(x-3\right)^{2}+4\left(x+1\right)^{2}.

$$\frac{9x^{2}-54x+81+4x^{2}+8x+4}{36}$$

Combine like terms in 9x^{2}-54x+81+4x^{2}+8x+4.

$$\frac{13x^{2}-46x+85}{36}$$