Answer each question. By what expression should we multiply ea...

Question

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

Accepted Answer

Welcome back. I am so glad you're here. We are asked what should be multiplied to each side of? Then we're given an equation. I'll write that in a moment so that the fraction form of the equation is removed. Our equation is on the left hand side of the equal sign, we have one fraction in the numerator. We have nine that's divided by, in the denominator, we have seven P multiplied by the quantity of five P plus 11. Now that is equal to, on the right hand side, we have two fractions. The first is X divided by seven P and then that's plus the second fraction which is Y divided by five P plus 11. Our answer choices are answer choice A P multiplied by the quantity of five P plus 11. Answer choice B seven P multiplied by the quantity of P plus 11. Answer choice C seven P multiplied by the quantity of five P plus 11. And answer choice D five P multiplied by the quantity of seven P plus 11. All right. So our goal here is to remove all of the fractions. And in order to do that, we are going to multiply everything here by the factors that occur in all of our denominators. So looking at the right hand side, we've got a seven P factor and then we have a different factor in the second fractions denominator, which is that five P plus 11. So we multiply the seven P by the quantity of five P plus 11. And if we look at the left hand side of the equal sign, that's exactly what the denominator is. And so when we multiply all of our numerators by seven P multiplied by the quantity of five P plus 11, all of the denominators will cancel out. Well, now you've got the answer. But let me show you how it works. So on the left hand side of the equal sign, we have that nine, which is now being multiplied by seven P and the quantity of five P plus 11 still all divided by seven P multiplied by the quantity of five P plus 11. That's equal to, on the right hand side, the first fraction we have X in the numerator. Now being multiplied by seven P multiplied by the quantity of five P plus 11. And that's all divided by seven P. And then plus the second fraction on the right hand side, we have that Y in the numerator. Now being multiplied by seven P and multiplied by the quantity of five P plus 11. And that's all divided by five P plus 11. Now, the glorious part where things cancel out the fraction on the left hand side of the equal sign, the seven PS cancel out and the five P plus elevens cancel out. First fraction on the right-hand side, the seven PS cancel out. And the second fraction on the right hand side, the five P plus elevens cancel out. And there you can see our denominators are gone, our fractions are gone. So we look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Answer each question. By what expression should we multiply each side of 5/((3x(2x + 1)) = A/(3x) + B/(2x + 1) so that there are no fractions in the equation?

Key Concepts

Least Common Denominator (LCD)

Partial Fraction Decomposition

Multiplying Equations to Clear Fractions

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