Solve 3a+2b/5a^2b+a+b/5ab-b-a/5a^2b

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

Evaluate

$$\frac{a^{2}+ab+4a+b}{5ba^{2}}$$

Short Solution Steps

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

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

Since \frac{3a+2b}{5ba^{2}} and \frac{\left(a+b\right)a}{5ba^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3a+2b+\left(a+b\right)a.

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

Since \frac{3a+2b+a^{2}+ba}{5ba^{2}} and \frac{b-a}{5a^{2}b} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3a+2b+a^{2}+ba-\left(b-a\right).

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

Combine like terms in 3a+2b+a^{2}+ba-b+a.

$$\frac{4a+b+a^{2}+ba}{5ba^{2}}$$

Expand

$$\frac{a^{2}+ab+4a+b}{5ba^{2}}$$

Short Solution Steps

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

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

Since \frac{3a+2b}{5ba^{2}} and \frac{\left(a+b\right)a}{5ba^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3a+2b+\left(a+b\right)a.

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

Since \frac{3a+2b+a^{2}+ba}{5ba^{2}} and \frac{b-a}{5a^{2}b} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3a+2b+a^{2}+ba-\left(b-a\right).

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

Combine like terms in 3a+2b+a^{2}+ba-b+a.

$$\frac{4a+b+a^{2}+ba}{5ba^{2}}$$