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Ket [755]
2 years ago
6

20 points!!

Mathematics
1 answer:
ANEK [815]2 years ago
5 0

See below for the proof of the equation \frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)

<h3>How to prove the equation?</h3>

The equation is given as:

\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)

Take the LCM

\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)

Expand

\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)

Evaluate the like terms

\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)

Rewrite as:

\frac{-2axy + 2bxy }{x^2 - y^2}= 2(a - b)

Factorize the numerator

\frac{2(a - b)(x^2 - y^2)}{x^2 - y^2}= 2(a - b)

Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation \frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b) has been proved

Read more about equations at:

brainly.com/question/2972832

#SPJ1

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