Solve ax+b/bx+bx-a/ax=

$$\frac { a x + b } { b x } + \frac { b x - a } { a x } =$$

Evaluate

$$\frac{a^{2}+b^{2}}{ab}$$

Short Solution Steps

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

$$\frac{\left(ax+b\right)a}{abx}+\frac{\left(bx-a\right)b}{abx}$$

Since \frac{\left(ax+b\right)a}{abx} and \frac{\left(bx-a\right)b}{abx} have the same denominator, add them by adding their numerators.

$$\frac{\left(ax+b\right)a+\left(bx-a\right)b}{abx}$$

Do the multiplications in \left(ax+b\right)a+\left(bx-a\right)b.

$$\frac{a^{2}x+ba+b^{2}x-ab}{abx}$$

Combine like terms in a^{2}x+ba+b^{2}x-ab.

$$\frac{a^{2}x+b^{2}x}{abx}$$

Factor the expressions that are not already factored in \frac{a^{2}x+b^{2}x}{abx}.

$$\frac{x\left(a^{2}+b^{2}\right)}{abx}$$

Cancel out x in both numerator and denominator.

$$\frac{a^{2}+b^{2}}{ab}$$

Expand

$$\frac{a^{2}+b^{2}}{ab}$$

Short Solution Steps

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

$$\frac{\left(ax+b\right)a}{abx}+\frac{\left(bx-a\right)b}{abx}$$

Since \frac{\left(ax+b\right)a}{abx} and \frac{\left(bx-a\right)b}{abx} have the same denominator, add them by adding their numerators.

$$\frac{\left(ax+b\right)a+\left(bx-a\right)b}{abx}$$

Do the multiplications in \left(ax+b\right)a+\left(bx-a\right)b.

$$\frac{a^{2}x+ba+b^{2}x-ab}{abx}$$

Combine like terms in a^{2}x+ba+b^{2}x-ab.

$$\frac{a^{2}x+b^{2}x}{abx}$$

Factor the expressions that are not already factored in \frac{a^{2}x+b^{2}x}{abx}.

$$\frac{x\left(a^{2}+b^{2}\right)}{abx}$$

Cancel out x in both numerator and denominator.

$$\frac{a^{2}+b^{2}}{ab}$$