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Question
If `a/b = c/d`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`.
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Solution
Let `a/b = c/d = k`
`=>` a = bk and c = dk
L.H.S = `(a^3c + ac^3)/(b^3d + bd^3)`
= `(ac(a^2 + c^2))/(bd(b^2 + d^2))`
= `((bk xx dk)(b^2k^2 + d^2k^2))/(bd(b^2 + d^2))`
= `(k^2 xx k^2(b^2 + d^2))/(b^2 + d^2)`
= k4
R.H.S = `(a + c)^4/(b + d)^4`
= `(bk + dk)^4/(b + d)^4`
= `[(k(b + d))/(b + d)]^4`
= k4
Hence `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`
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