Question

If a/4 = b/5 = c/3 then , then prove that: (a - b + c)/(a + b - c) = 1/3​

Answer 1

To prove (a - b + c)/(a + b - c) = 1/3, substitute the given values of a, b, and c into the equation and simplify. Cancel out like terms to show that both sides of the equation are equal to 1.

Step-by-step explanation:

To prove that (a - b + c)/(a + b - c) = 1/3, we can first rewrite the given equations as:

a/4 = b/5 = c/3

From these equations, we can conclude that:

a = 4b/5

b = 5c/3

Substituting these values into the expression (a - b + c)/(a + b - c) gives:

(4b/5 - 5c/3 + c)/(4b/5 + 5c/3 - c)

Combine the fractions and simplify:

(4b/5 - 15c/15 + 15c/15)/(4b/5 + 15c/15 - 15c/15)

(4b - 15c + 15c)/(4b +15c - 15c)

Cancel out like terms:

4b/4b = 15c/15c

1 = 1

Therefore, (a - b + c)/(a + b - c) = 1/3 is proven.