Perform the indicated operation, and write each answer in lowe...

Question

Perform the indicated operation, and write each answer in lowest terms. 2x/5 + x/4

Accepted Answer

Hey everyone for the following expression were asked to perform addition to simplify the answer. Were given 15 H. Over seven plus H. Over three. Alright so let's just rewrite what were given 15 H. Divided by seven plus H. Divided by three. Okay now when you're given expressions like this and they have variables H. Like H. And M. Okay don't get worried. This is you're going to treat this exactly how you would treat adding fractions when they're just numbers. Okay so we're adding fractions. What we wanna do is we want to find a common denominator. Okay so we're gonna do the same thing we would normally do here. So we see that we have a denominator of seven in the first term. A denominator of three in the seconds. We want to find the lowest Common denominator. Okay so what's that going to be? Well it's gonna be 21. Okay if we multiply the 27 times three we're gonna get 21. So in order to have 21 in our left hand turn we're gonna need to multiply the denominator by three. Okay if we multiply the denominator by three we have to multiply the numerator by three as well. So we have 15 h. Times three divided by seven times three. Okay that's our first term and you'll notice that now you see that we're multiplying the whole term by three divided by three. That's just multiplying by one which we know. Doesn't change our function or expression. Okay. Alright then we do the second term. Now it has a denominator of three. We want to turn this into 21. So we need to multiply by seven. So we're gonna have a church times seven divided by three times seven. Okay and again we're multiplying by 7/7. That's just one. We're not changing our expression. Alright so let's just simplify and kind of multiply out these terms. So in the numerator of the first term we're going to get 45 h. And in the denominator we have divided by 21 the second term we're going to have seven H. Again divided by 21. So now we have our common denominator. We know if we have a common denominator we can put these terms together add the numerator and keep the common denominator. So this is going to be equal to 45 H. Plus seven H. All divided by 21 and 45 H plus seven H. That is going to give us 52 H. K. Divided by 21. That's as simple as we can get it. And so our expression, our simplified expression is going to be 52 h. divided by 21. If we look at our answer choices that is going to be answer choice. D Thanks everyone for watching. I hope this video helped see you in the next one

Perform the indicated operation, and write each answer in lowest terms. 2x/5 + x/4

Key Concepts

Adding Rational Expressions

Finding the Least Common Denominator (LCD)

Simplifying Fractions

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