Add or subtract, as indicated. See Example 4. (1/(x + z)) + (1...

Question

Add or subtract, as indicated. See Example 4. (1/(x + z)) + (1/(x - z))

Accepted Answer

Welcome back everyone. In this problem, we want to simplify the expression nine divided by the expression M plus H plus nine divided by the expression M minus H. For our answer choices A is 18 M divided by the product of the expressions M plus H and M minus H B is negative A and M divided by that same expression C is 18 H and D is negative 18 H. And both of those are being divided by the expression. Now, what do we know here? Well, it says we want to simplify our expression. So I'm going to write our expression right here. Nine divided by M plus H plus nine divided by M minus H. And now we're going to treat our fraction even though it's denominator is an algebraic expression still as a fraction because it's still a fraction, right? So first, let's think what is the lowest common multiple of M plus H and M minus H? Well, that LCM would be M plus H multiplied by M minus H because both of these terms can go into that denominator and it's the lowest common multiple for both. So let's go ahead and rewrite our fractions with that denominator M plus H multiplied by M minus H. Now M plus H into M plus H multiplied by M minus H equals M minus H. So we can multiply the numerator by M minus H. So our, the numerator for our first fraction, our first expression or co would have been nine multiplied by M minus H next M minus H into M plus H multiplied by M minus H goes M plus H times. So we'd multiply nine by M plus H for our second co now let's go ahead and simplify nine, multiplied by M is nine M and multiplied by negative H is negative nine H and nine multiplied by M is nine M nine, multiplied by H is nine H and all of that is being divided by the same denominator. Now, are there any common terms here that we can use to simplify? Well, yeah, there are notice that we have nine H, let me, let me circle them with a different color. So we have nine H and negative nine H and then we have nine M and positive nine M no, negative nine H plus nine H equals zero. They cancel each other out and nine M plus nine M equals 18 M. That's our final answer in its simplest form, which would be 18 M divided by the product of the expressions M plus H and M minus H. And when we look in our answer choices that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

Add or subtract, as indicated. See Example 4. (1/(x + z)) + (1/(x - z))

Key Concepts

Adding and Subtracting Rational Expressions

Factoring and Simplifying Algebraic Expressions

Difference of Squares

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