Solve ( e) (- a + 2b)/(a - b) - (b - 2a)/(a - b) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac { - a + 2 b } { a - b } - \frac { b - 2 a } { a - b }$$

Evaluate

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

Short Solution Steps

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

$$\frac{-a+2b-\left(b-2a\right)}{a-b}$$

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

$$\frac{-a+2b-b+2a}{a-b}$$

Combine like terms in $-a+2b-b+2a$.

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

Expand

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

Short Solution Steps

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

$$\frac{-a+2b-\left(b-2a\right)}{a-b}$$

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

$$\frac{-a+2b-b+2a}{a-b}$$

Combine like terms in $-a+2b-b+2a$.

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