Add the following expressions and simplify if possible:3x+2x+2\frac{3}{x}+\frac{2}{x+2}

5 x + 6 x ( x + 2 ) \frac{5x+6}{x\left(x+2\right)}

Add the following expressions and simplify if possible: 3 x + 2 x + 2 \frac{3}{x}+\frac{2}{x+2}

this problem, we are asked to add the following expressions and to simplify if possible. Now when adding rational expressions, like I can see I have in this problem, what I need to do is get a common denominator. Now it's clear that x and x plus two are not the same thing. But I can get a common denominator by first figuring out the LCD, the least common denominator. That's going to be the product of all unique prime factors that we have. And I can see that we have an x, which is unique by itself. I also see that we have an x plus two, which is unique. So x times x plus two would be my LCD. Now what I need to do is multiply the numerator and denominator of each of these rational expressions by the missing factor that we have. So starting with three over x, I can see that we don't have an x plus two. We have an x there, but not an x plus two. So what I'm going to do is I'm going to take my three over x, and I'm going to multiply the numerator and denominator by x plus two, which will give me something that looks like this. Now what I'm going to do is add this to this rational expression, and I'm going to multiply the numerator and denominator by the missing factor. We have an x plus two in the denominator here, and so what I'm missing is this x, so that means I need to multiply the numerator and denominator by x. Now, this fraction, if I can go ahead and take this three and distribute it into these parentheses, that's gonna give me three times x plus, and then we'll have three times two, which is six, all over x times x plus two. Now if I go over to this other rational expression, we're going to have two times x, which is two x, and it's going to be over x times x plus two. Notice I now have a common denominator, so I can just add the numerators directly across. So I have three x plus two x, which gives us five x plus six, all over x times x plus two. And this right here is the simplified solution to the problem where we added these two rational expressions. Hope you found this video helpful.

Add the following expressions and simplify if possible: 3 x + 2 x + 2 \frac{3}{x}+\frac{2}{x+2}

5 x + 6 x ( x + 2 ) \frac{5x+6}{x\left(x+2\right)}

5 x + 4 x ( x + 2 ) \frac{5x+4}{x\left(x+2\right)}

8. Rational Expressions and Equations

Adding and Subtracting Rational Expressions with Different Denominators

Beginning Algebra

8. Rational Expressions and Equations

Adding and Subtracting Rational Expressions with Different Denominators

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Multiple Choice

Add the following expressions and simplify if possible:
$\frac{3}{x} + \frac{2}{x + 2}$

$\frac{5 x + 6}{x (x + 2)}$

$\frac{11}{x + 2}$

$\frac{5 x + 4}{x (x + 2)}$

$\frac{9}{x + 2}$

Verified step by step guidance

Identify the two fractions to be added: $\frac{3}{x}$ and $\frac{2}{x+2}$.

Find the least common denominator (LCD) for the two fractions. Since the denominators are $x$ and $x+2$, the LCD is $x \times (x+2)$.

Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator appropriately: $\frac{3}{x} = \frac{3(x+2)}{x(x+2)}$ and $\frac{2}{x+2} = \frac{2x}{x(x+2)}$.

Add the numerators over the common denominator: $\frac{3(x+2) + 2x}{x(x+2)}$.

Simplify the numerator by distributing and combining like terms: \$3x + 6 + 2x = 5x + 6$, so the expression becomes $\frac{5x + 6}{x(x+2)}$.

8:03m

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Master Adding and Subtracting Rational Expressions with Unlike Denominators Example 1 with a bite sized video explanation from Patrick Ford

Struggling with Beginning Algebra?

Add the following expressions and simplify if possible:3x+2x+2\(\frac{3}{x}\)+\(\frac{2}{x+2}\)

Watch next

Add the following expressions and simplify if possible:
$\frac{3}{x} + \frac{2}{x + 2}$