Make K the subject of the relation T = {TK - H/K - H}

Correct Answer is : K = H(T2−1)T2−TH(T² - 1)/T² - TT2−TH(T2−1)

Correct Answer is : K = H(T2−1)T2−TH(T² - 1)/T² - TT2−TH(T2−1)

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WAEC Mathematics 2015 Paper

Question : 31

Total: 45

\sqrt{\frac{TK - H}{K - H}}

Solution:

Concept:

Squaring both sides removes the square root, then rearrange terms to factor out

K

Explanation:

Start with the given relation:

T = \sqrt{\frac{TK - H}{K - H}}

Square both sides to eliminate the square root:

T^2 = \frac{TK - H}{K - H}

Multiply both sides by

(K - H)

T^2(K - H) = TK - H

Expand the left side:

T^2K - T^2H = TK - H

Collect the terms containing

K

on one side:

T^2K - TK = T^2H - H

Factor out

K

on the left and

H

on the right:

K(T^2 - T) = H(T^2 - 1)

Divide both sides by

(T^2 - T)

K = \frac{H(T^2 - 1)}{T^2 - T}

Answer:

K = \frac{H(T^2 - 1)}{T^2 - T}

This matches option A.

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