Question

2a + 2b - 3c - 3d / 2a - 2b - 3c - 3d = a+ b - 4c - 4d / a-b-4c+4d​

Answer 1

Answer:

Presuming that is:

(2a + 2b - 3c - 3d) / (2a - 2b - 3c + 3d) = (a + b - 4c - 4d) / (a - b - 4c + 4d)

Then to get it to: a / b = c / d

Let's cross multiply this to see what we get:

(2a + 2b - 3c - 3d)(a - b - 4c + 4d) = (a + b - 4c - 4d)(2a - 2b - 3c + 3d)

Now expand, then we can see what cancels out:

2a² - 2ab - 8ac + 8ad + 2ab - 2b² - 8bc + 8bd - 3ac + 3bc + 12c² - 12cd - 3ad + 3bd + 12cd - 12d² =

2a² - 2ab - 3ac + 3ad + 2ab - 2b² - 3bc + 3bd - 8ac + 8bc + 12c² - 12cd - 8ad + 8bd + 12cd - 12d²

combining like terms:

2a² - 11ac + 5ad - 2b² - 5bc + 11bd + 12c² - 12d² =

2a² - 11ac - 5ad - 2b² + 5bc + 11bd + 12c² - 12d²

Now we can add -2a² + 2b² - 12c² + 12d² to both sides to cancel them out:

-11ac + 5ad - 5bc + 11bd = -11ac - 5ad + 5bc + 11bd

Add 11ac - 11bd to both sides:

5ad - 5bc = -5ad + 5bc

Divide both sides by 5:

ad - bc = -ad + bc

Let's add (ad + bc) to both sides:

2ad = 2bc

Divide both sides by 2:

ad = bc

And divde both sides by (bd)

a/b = c/d

It took some weird multiplication of polynomials, but it did work out.

answered by toppr

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