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The value of a/(a-b)+b/(b-a) is...

The value of `a/(a-b)+b/(b-a)` is

A

`((a+b))/((a-b))`

B

`-1`

C

`2ab`

D

1

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \( \frac{a}{a-b} + \frac{b}{b-a} \), we can follow these steps: ### Step 1: Rewrite the second term Notice that \( b-a \) can be rewritten as \( -(a-b) \). Thus, we can rewrite the second term: \[ \frac{b}{b-a} = \frac{b}{-(a-b)} = -\frac{b}{a-b} \] ### Step 2: Combine the fractions Now, we can combine the two fractions: \[ \frac{a}{a-b} + \left(-\frac{b}{a-b}\right) = \frac{a - b}{a-b} \] ### Step 3: Simplify the expression Since the numerator and the denominator are the same (as long as \( a \neq b \)), we can simplify: \[ \frac{a-b}{a-b} = 1 \] ### Final Answer Thus, the value of \( \frac{a}{a-b} + \frac{b}{b-a} \) is: \[ \boxed{1} \] ---
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