Add or subtract, as indicated. (7x + 8)/(3x + 2) - (x + 4)/(3x...

Question

Add or subtract, as indicated. (7x + 8)/(3x + 2) - (x + 4)/(3x + 2)

Accepted Answer

Hello, today we're going to be simplifying the given expression. So what we are given is the quantity two G plus 5/3 G minus five minus five G plus all over three G minus five. Now, in order to subtract two fractions together, we need to have the same denominators. But notice that both of the given fractions have three G minus five as its denominator. So we can go ahead and combine this into a single fraction by combining the numerator is together and doing that is going to give us two G plus five minus the quantity five G plus and that's going to be over three G minus five. Now, in order to simplify the numerator, we're going to distribute the negative one into the quantity five G plus 32. And that's going to give us two G plus five minus five G minus 32 all over three G minus five. Now combining the light terms together two G minus five G is going to give us negative three G and five minus 32 is going to give us negative 27. So what we have in the numerator is -3G - all over 3G -5. And one thing to note about the numerator, since both of the terms are negative, we can go ahead and factor out a negative from the numerator. And doing so is going to give us negative three G plus all over three G minus five. Now, typically we like to represent our simplified answer with a positive numerator. So in order to turn the numerator positive, we can go ahead and reorder the denominator. If we switch the positions of three G and negative five in the denominator, we can rewrite this as negative three G plus all over negative five plus three G. And if I want this negative five to be positive, I can go ahead and factor out a negative one from the, from the denominator factory. Now a negative one from the denominator is going to give me the expression negative three G plus 27 all over negative five minus three G. And now notice that we have a negative quantity over a negative quantity. Whenever you divide a negative quantity by another negative quantity, it gives you a positive quantity. So this is going to simplify to give us three G plus 27/5 minus three G. And this is going to be the rationalized form or the simplified form of the given expression. And with that being said, the answer to this problem is going to be D 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. (7x + 8)/(3x + 2) - (x + 4)/(3x + 2)

Key Concepts

Like Denominators in Rational Expressions

Combining Like Terms in the Numerator

Simplifying Rational Expressions

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