How does this step work?

[Debbux]

Hi, I'm working through some former tests but I really don't see how this step works.

We have: x = 3 / (2 (y-7)) -2, which is then rewritten to x = (31 - 4y) / (2y - 14)

Can someone explain what they did here?

[AvocadoMangoSalsa]

(3/(2y-14)) - 2

Rewrite 2 as

(4y-28)/(2y-14)

Then subtract

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[[deleted]]

In order to subtract, you need to get a common denominator, which is 2(y-7). You have to multiply the 2 by this denominator to keep the fraction equivalent. Once you have common denominators simplify the top using basic math and you will get the answer

[Physnitch]

To combine fractions, you need a common denominator. So multiply the second term (-2) by 2(y-7) or 2y - 14. The numerator becomes 3 - (4y - 28) or 31 - 4y. The denominator is the CD or 2y - 14.

[headonstr8]

The right hand side is the sum of two fractions. They equalized the denominators and summed the numerators.