Add or subtract, as indicated. (17y + 3)/(9y + 7) - (-10y - 18...

Question

Add or subtract, as indicated. (17y + 3)/(9y + 7) - (-10y - 18)/(9y + 7)

Accepted Answer

Hello, today we're gonna be simplifying the given expression. So what we are given is two G plus 5/3 G minus one minus the quantity negative five G minus 32/3 G minus one. Now, in order to subtract two fractions together, we need to make sure that both of the fractions have the same denominator. But in this case, we have the quantity three G minus one in both of the fractions. So we can go ahead and combine this expression as a single rational expression by combining the numerators together. And that's going to give us two G plus five minus the quantity negative five G minus 32 all over three G minus one. Now, in order to simplify the numerator, the numerator, I'm going to have to multiply negative one into the quantity negative five G minus 32. And that's going to give me two G plus five plus five G plus 32 all over three G minus one. And now I just need to go ahead and combine the like terms together. Two G plus five G is going to give me seven G and 32 plus five is going to give me 37. So the numerator is going to simplify to seven G plus 37 and that's going to be over three G minus one, which is going to be the simplified version of the given expression. And with that being said, the answer to this problem is going to be C so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Add or subtract, as indicated. (17y + 3)/(9y + 7) - (-10y - 18)/(9y + 7)

Key Concepts

Like Denominators in Rational Expressions

Combining Like Terms in the Numerator

Simplifying Rational Expressions

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