Converting to the LCD

[sofrustrated52]

Not sure what I am supposed to do here. It says to find the lcd for the given rational expression and convert rational expression into an equivalent rational expression with the lcd as the denominator. 4/x-y,5x/2y-2x
I have no idea where to begin and a step-by-step instruction would be greatly appreciated.

 

[mmm4444bot]

find the lcd for the given rational expression

4/x-y,5x/2y-2x

The exercise could be better worded. There are two expressions.

They probably want you to rewrite the first given expression, such that the new ratio has the lowest common denominator between the two given ratios.

At this point, I will mention that we need to type grouping symbols around the denominator, when typing algebraic ratios using a keyboard. Normally, the horizontal fraction bar serves as the grouping symbol, in mathematical typesetting, but it's too much bother to "draw" fraction bars by typing. (We can format mathematical typesetting here using LaTex, as shown below, but it's easier typing the parentheses.)

The rational expression \(\displaystyle \frac{4}{x - y}\) is typed as 4/(x - y)

The algebraic ratio \(\displaystyle \frac{5x}{2(y - x)}\) is typed as 5x/[2(y - x)]

Typing 4/x - y actually means \(\displaystyle \frac{4}{x} - y\)

I'll assume that you understand the concept of LCDs that you learned when doing arithmetic with fractions.

EG:

4/7 and 5/14, rewrite 4/7 with the LCD between the two:

LCD is 14, so we multiply 4/7 by 2/2 to get 8/14.

By what do we need to multiply the expression x - y to get 2y - 2x ?

If you then multiply the top and bottom of 4/(x - y) by that factor, you'll have an equivalent ratio with the LCD.