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Algebra and Applications Test 2

Question : 9 of 40

Marks: +1, -0

u^2 = gv + hw

v^2 = fu + w^2 = fu + gv

\frac{1}{u+f} + \frac{g}{v+g} + \frac{h}{w+h}

equal to?

Solution: 👈: Video Solution

Concept:

Use the given relations to express each fraction over the same denominator.

Explanation:

Let

S = fu+gv+hw

From

u^2 = gv+hw

, add

fu

to both sides:

u^2+fu = fu+gv+hw = S

u(u+f)=S

, hence

\frac{f}{u+f} = \frac{fu}{S}

From

v^2 = hw+fu

, add

gv

to both sides:

v^2+gv = fu+hw+gv = S

v(v+g)=S

, hence

\frac{g}{v+g} = \frac{gv}{S}

From

w^2 = fu+gv

, add

hw

to both sides:

w^2+hw = fu+gv+hw = S

w(w+h)=S

, hence

\frac{h}{w+h} = \frac{hw}{S}

Adding the three fractions:

\frac{f}{u+f}+\frac{g}{v+g}+\frac{h}{w+h} = \frac{fu+gv+hw}{S} = \frac{S}{S}=1

Answer:

The expression equals

1

, so the correct option is B.

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