Solve a+b/3x-a-b/4x+a^2+b^2/5x

$$\frac { a + b } { 3 x } - \frac { a - b } { 4 x } + \frac { a ^ { 2 } + b ^ { 2 } } { 5 x }$$

Evaluate

$$\frac{12a^{2}+12b^{2}+5a+35b}{60x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 4x is 12x. Multiply \frac{a+b}{3x} times \frac{4}{4}. Multiply \frac{a-b}{4x} times \frac{3}{3}.

$$\frac{4\left(a+b\right)}{12x}-\frac{3\left(a-b\right)}{12x}+\frac{a^{2}+b^{2}}{5x}$$

Since \frac{4\left(a+b\right)}{12x} and \frac{3\left(a-b\right)}{12x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(a+b\right)-3\left(a-b\right)}{12x}+\frac{a^{2}+b^{2}}{5x}$$

Do the multiplications in 4\left(a+b\right)-3\left(a-b\right).

$$\frac{4a+4b-3a+3b}{12x}+\frac{a^{2}+b^{2}}{5x}$$

Combine like terms in 4a+4b-3a+3b.

$$\frac{a+7b}{12x}+\frac{a^{2}+b^{2}}{5x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12x and 5x is 60x. Multiply \frac{a+7b}{12x} times \frac{5}{5}. Multiply \frac{a^{2}+b^{2}}{5x} times \frac{12}{12}.

$$\frac{5\left(a+7b\right)}{60x}+\frac{12\left(a^{2}+b^{2}\right)}{60x}$$

Since \frac{5\left(a+7b\right)}{60x} and \frac{12\left(a^{2}+b^{2}\right)}{60x} have the same denominator, add them by adding their numerators.

$$\frac{5\left(a+7b\right)+12\left(a^{2}+b^{2}\right)}{60x}$$

Do the multiplications in 5\left(a+7b\right)+12\left(a^{2}+b^{2}\right).

$$\frac{5a+35b+12a^{2}+12b^{2}}{60x}$$

Expand

$$\frac{12a^{2}+12b^{2}+5a+35b}{60x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 4x is 12x. Multiply \frac{a+b}{3x} times \frac{4}{4}. Multiply \frac{a-b}{4x} times \frac{3}{3}.

$$\frac{4\left(a+b\right)}{12x}-\frac{3\left(a-b\right)}{12x}+\frac{a^{2}+b^{2}}{5x}$$

Since \frac{4\left(a+b\right)}{12x} and \frac{3\left(a-b\right)}{12x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(a+b\right)-3\left(a-b\right)}{12x}+\frac{a^{2}+b^{2}}{5x}$$

Do the multiplications in 4\left(a+b\right)-3\left(a-b\right).

$$\frac{4a+4b-3a+3b}{12x}+\frac{a^{2}+b^{2}}{5x}$$

Combine like terms in 4a+4b-3a+3b.

$$\frac{a+7b}{12x}+\frac{a^{2}+b^{2}}{5x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12x and 5x is 60x. Multiply \frac{a+7b}{12x} times \frac{5}{5}. Multiply \frac{a^{2}+b^{2}}{5x} times \frac{12}{12}.

$$\frac{5\left(a+7b\right)}{60x}+\frac{12\left(a^{2}+b^{2}\right)}{60x}$$

Since \frac{5\left(a+7b\right)}{60x} and \frac{12\left(a^{2}+b^{2}\right)}{60x} have the same denominator, add them by adding their numerators.

$$\frac{5\left(a+7b\right)+12\left(a^{2}+b^{2}\right)}{60x}$$

Do the multiplications in 5\left(a+7b\right)+12\left(a^{2}+b^{2}\right).

$$\frac{5a+35b+12a^{2}+12b^{2}}{60x}$$