SOLUTION: could someone help me work this out step by step so I can understand it. I am lost.I am suppose to build up the rational expression into an equivalent rational expression with the

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Question 383500: could someone help me work this out step by step so I can understand it. I am lost.I am suppose to build up the rational expression into an equivalent rational expression with the indicated denominator. Please help.
Thank you
-7yt/3x=?/18xyt

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
-7yt/3x=?/18xyt
it helps to separate what is being multiplied by each other by *.

it also helps to surround operations that are going to be performed together by parentheses.

your formula becomes:

(-7*y*t) / (3*x) = ? / (18*x*y*t)

multiply both sides of this equation by (18*x*y*t)

you get:
(18*x*y*t) * ((-7*y*t) / (3*x)) = ?

since a * (b/c) = (a*b) / c, then your expression above is equivalent to:

((18*x*y*t) * (-7*y*t)) / (3*x) = ?

(18*x*y*t) * (-7*y*t) is equal to (-126 * x * y^2 * t^2)

this is because 18 * -7 = -126 and y * y = y^2 and t * t = t^2.

(-126 * x * y^2 * t^3) / (3 * x) is equal to (-42 * y^2 * t^2)

this is because -126/3 = -42 and x/x = 1 which is not shown but implied.

your answer should be ? = (-42 * y^2 * t^2)

you can confirm it by assigning values to each of the variables at random and seeing if the final expression is true after simplification.

Assume x = 2, y = 3, t = 4

your original expression of (-7*y*t) / (3*x) = ? / (18*x*y*t) becomes (-7*y*t) / (3*x) = (-42 * y^2 * t^2) / (18*x*y*t) which becomes (-7*3*4) / (3*2) = (-42 * 3^2 * 4^2) / (18*2*3*4)

this resolves to -84/6 = -6048 / 432 which resolves finally to -14 = -14 confirming that we did the calculations correctly.