Ratio-algebraic method-tenth grade-8

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If a/b = c/d, then show that fraction (a + c) / (b + d) is equal to either.
Similarly, prove that (a - c) / (b - d) is equal to either fraction.

Solution: Ler a/b = c/d = k

Then a = bk

c = dk

Adding, a + c = k(b + d)

Therefore, k = (a + c) / (b + d)

i.e. a/b = c/d = (a + c) / (b + d)

Again let a/b = c/d = k

Therefore, a = bk

c = dk

Subtracting a - c = k(b - d)

Therefore, k = (a - c) / (b - d)

Therefore, a/b = c/d = (a - c) / (b - d)