If \sqrtt=\sqrtu+\sqrtv what is the simplified value of (\frac{t+u-v}{t-u+v})^2?

Algebra and Applications Test 2

Question : 23 of 40

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√t=√u+√v

what is the simplified value of

({t+u-v}/{t-u+v})^2?

Solution:

√t=√u+√v

({t+u-v}/{t-u+v})^2

=({ (√u+√v)^2+u-v}/{ (√u+√v)-u+v})^2

=({u+v+2√{uv}+u-v}/{u+v+2√{uv}-u+v})^2

=({2√u (√u+√v)}/{2√v(√u+√v)})^2

=u/v

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