Question

I am having issues with a math problem. I need to find the common denominator of the following algebraic expressions.

Answer 1

\[\frac{ x ^{2}-49 }{ 2x-1 }\]\[\frac{x ^{2}-14x+49 }{ 1-2x }\]

Answer 2

I think that the answer is \[x^{3}*2+x^{2}\]

Answer 3

But after that, I don't understand how to build up the fractions.

Answer 4

the denominators are 2x-1 and 1-2x

Answer 5

notice how we can factor 1-2x to get

1-2x

-1(-1+2x)

-1(2x-1)

Answer 6

so what does that mean?

Answer 7

Honestly, I am not sure what it means. When I look at it, it looks like to me that the expressions are pretty much the same and that both denominators are the same thing written different ways.

Answer 8

we have 2x-1 and -1(2x-1)

Answer 9

the first denominator is missing the -1 out front

Answer 10

Okay so I would then multiply it by -1get that?

Answer 11

so if you were to multiply top and bottom of the first fraction by -1, that gets both denominators equal to the LCD

Answer 12

yep

Answer 13

Okay, so then how do I "build up" the expressions so that the denominators are the same? multiply the whole expression with 2x-1 as the denominator by -1?

Answer 14

correct, you multiply top and bottom of the first fraction by -1

Answer 15

you do both top and bottom to balance things out

Answer 16

Okay. I think I get it now. Thank you

Answer 17

yw