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UPTET Paper 2 Math and Science 2019 Solved Paper

Question : 120 of 120

Marks: +1, -0

\frac{x}{x-z}+\frac{z}{y-z}

Solution:

Concept:

Use the given relation

x + y = 2z

to simplify the algebraic fraction by taking LCM and substituting.

Explanation:

Start with

\frac{x}{x-z} + \frac{z}{y-z}

Take LCM:

\frac{x(y-z) + z(x-z)}{(x-z)(y-z)}

Expand numerator:

xy - xz + zx - z^{2} = xy - z^{2}

Denominator:

(x-z)(y-z) = xy - xz - yz + z^{2}

Rewrite denominator as

xy - z(x+y) + z^{2}

Use

x+y = 2z

: denominator becomes

xy - z(2z) + z^{2} = xy - 2z^{2} + z^{2} = xy - z^{2}

Now numerator = denominator =

xy - z^{2}

, so the fraction equals

1

Answer:

A. 1

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