Algebra and Applications Test 1

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Question : 3 of 40

Marks: +1, -0

If

x + y = 2z

then the value of

x/{ x-z}+z/{y-z}

is:

1
3
$1 / 2$
2

Solution:

We have

x + y = 2z

x/{ x-z}+z/{y-z}

{x(y-z)+z(x-z)}/{(x-z)(y-z)}

={xy-zx+zx-z^2}/{xy-zy-zx-z^2}

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

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

={xy -z^2}/{xy- 2z^2-z^2}

={xy -z^2}/{xy- z^2 }=1

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