Algebraic Merging: Solve this Equation with 100% Precision!#shorts #short #algebra

Welcome to another math breakdown! Today, we are tackling a classic algebraic rational expression.

The Problem:
If $x + y = 2a$, what is the exact value of $\frac{a}{x-a} + \frac{a}{y-a}$?

Forget about plugging in random numbers or making structural predictions. We demand 100% precision, solving this strictly from first principles through pure Algebraic Merging. No guesswork, no known values—just rigorous derivation.
Step-by-Step Derivation:Find a common denominator to merge the terms:$$\frac{a(y-a) + a(x-a)}{(x-a)(y-a)}$$

Expand the numerator:$$ay - a^2 + ax - a^2 = a(x + y) - 2a^2$$

Substitute our given equation ($x + y = 2a$) into the numerator:$$a(2a) - 2a^2 = 2a^2 - 2a^2 = 0$$

Since the numerator is exactly $0$ (and assuming the denominator $xy - a^2 \neq 0$), the entire expression evaluates to $0$.

The correct answer is (b) 0.

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Видео Algebraic Merging: Solve this Equation with 100% Precision!#shorts #short #algebra канала Maths mind