Simplify each complex fraction. [ 1/(y+3) - 1/y ] / (1/y)

Question

Accepted Answer

Hey everyone here we are asked to simplify the following expression where we have two divided by M plus seven plus two divided by M. And this is all divided by two divided by M. So now our first step here in simplifying this expression is to first combine the two fractions in the numerator into one fraction in this me that we first need to get a common denominator between these two fractions. So taking the first fraction in our numerator, we need to multiply both the numerator and the denominator by the value in the denominator of the other fraction. So doing this we take the fraction two divided by M plus seven. And we multiply the numerator and the denominator by em and now moving on to our second fraction where we have two divided by M. Here we need to multiply the numerator and the denominator by the denominator of the first fraction. So we multiply the numerator and the denominator by M plus seven. And again this whole expression is still divided by two divided by M. And so now we just need to start simplifying our numerator. So performing this, these multiplication steps here we have two M divided by M times the quantity of M plus seven plus our second fraction here where we will have two times the quantity of em plus seven divided by M times the quantity of M plus seven. And again this whole expression is divided by two divided by M. And now we need to just continue to simplify our numerator here. So we have now since we have a common denominator between the two fractions in the numerous, we can just combine their to enumerators. So doing this we have to M plus two M. From factoring in the two plus 14. All divided by M. Times equality of M plus seven. And this is all divided by two divided by M. So now we can just finish up simplifying our numerator here, so our expression becomes four M plus 14. All divided by M times the quantity of M plus seven, all divided by two divided by M. So now we can continue to simplify this expression by taking the denominator here which is two divided by M. And since we're dividing by a fraction we can actually multiply by the reciprocal of this denominator, so doing this, our expression becomes four M plus 14. All divided by M times the quantity of M plus seven times the reciprocal of our denominator which is just M divided by two. And now we can do some simplifications here. We see that we have an M. In our first denominator and we also have an M. In our second numerator. So simplifying our expression becomes four M plus 14, all divided by two times the quantity of M plus seven. And now to continue to simplify we need to factor out a two from both of the terms in our numerator. So we get two times the quantity of two M plus seven, all divided by two times the quantity of M plus seven. And now we can clearly see that we have a two in the numerator and in the denominator. So they both cancel. And with this we are left with our final simplified expression of the quantity of two M plus seven divided by the quantity of M plus seven. And with this we are left with our final answer here, which is answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Simplify each complex fraction. [ 1/(y+3) - 1/y ] / (1/y)

Key Concepts

Complex Fractions

Common Denominator

Simplifying Expressions

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