What is a/(2a-b)+(3a-b)/(b-2a) ?

The solution to a/(2a-b)+(3a-b)/(b-2a) is -1

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simplify a/(2a-b)+(3a-b)/(b-2a)

simplify

\frac{a}{2 a - b} + \frac{3 a - b}{b - 2 a}

- 1

Solution steps

\frac{a}{2 a - b} + \frac{3 a - b}{b - 2 a}

Factor

b - 2 a : - (2 a - b)

= \frac{a}{2 a - b} + \frac{3 a - b}{- ( 2 a - b )}

Least Common Multiplier of

2 a - b, - (2 a - b) : - (2 a - b)

Adjust Fractions based on the LCM

= \frac{- a}{- ( 2 a - b )} + \frac{3 a - b}{- ( 2 a - b )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{- a + 3 a - b}{- ( 2 a - b )}

Add similar elements:

- a + 3 a = 2 a

= \frac{2 a - b}{- ( 2 a - b )}

Cancel the common factor:

2 a - b

= \frac{1}{- 1}

Apply the fraction rule:

\frac{a}{- 1} = - a

= - 1

2 x^{2} - 44 x + 242

3 x + 14 = 7 x - 6

\frac{2}{3} = \frac{x}{5}

9 k^{2} = 225

\frac{8 - 7 i}{1 - 2 i}