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# Write the following as a single rational expression

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A. Write the following as a single rational expression:

B. What are the restricted value(s) of y for the rational expression to be defined:

C. Reduce the following expression to lowest terms:

D. Simplify the following expression:

https://brainmass.com/math/basic-algebra/following-single-rational-expression-159547

## SOLUTION This solution is FREE courtesy of BrainMass!

A. Write the following as a single rational expression:
= (2x^2 (10b^3k) + a^2u^2(5ab) ) / ((5ab)(10b^3k))
= (20x^2b^3k + 5a^3u^2b) / (50ab^4k)
= (20x^2b^2k + 5a^3u^2) / (50ab^3k) (dividing both numerator and denominator by 'b')

B. What are the restricted value(s) of y for the rational expression to be defined:
The expression will not be defined if the denominator is 0

9y+7 = 0, so y = -7/9

C. Reduce the following expression to lowest terms:

=3(t^2-1) / (t^2 - 5t + t - 5)
= 3 (t+1) (t-1) / (t+1) (t-5)
= 3(t-1) / (t-5)
= (3t - 3) / (t-5)

D. Simplify the following expression:

= 2 sqrt ( 3x3 x 8 ) x sqrt ( 7x7x2)
= 2 x 3 sqrt(8) x 7 x sqrt(2)
= 42 x sqrt (8 x 2)
= 42x 4
= 168

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