If t=\frac{gh}{g+h}, u=\frac{gi}{g+i} and v=\frac{ hi}{ h+i} where t, u and v are non-zeros, then what is g equal to?

Correct Answer is : 2tuvtv+uv−tu

Algebra and Applications Test 1

Question : 17 of 40

Marks: +1, -0

t={gh}/{g+h}, u={gi}/{g+i}

and

v={ hi}/{ h+i}

where t, u and v are non-zeros, then what is g equal to?

Solution:

∵ t={gh}/{g+h}, u={gi}/{g+i}

and

v={ hi}/{ h+i}

Check these values for each given option.

∴{2tuv}/{tv +uv- tu}

={{2g^2h^2i^2}/{(g+h)(h+i)(h+g)}}/{{ghi(h(g+i)+i(g+h)-g(h+i))}/{(g+h)(h+i)(h+g)}}

={2ghi}/{gh+hi+ig+ig-gh-hi}

={2ghi}/{2hi}=g

g={2tuv}/{tv +uv- tu}

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