In this video, we are going to solve fractional equations, such as $\frac{4}{x} + \frac{2}{6} = \frac{5}{x}$, by using the least common denominator.

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For example: $\frac{4}{x}+\frac{2}{6}=\frac{5}{x}$, find the value of x

First, find the least common denominator, which is 6x. Multiple every numerator by 6x $\frac{(6x)4}{x}+\frac{(6x)2}{6}=\frac{(6x)5}{x}$

The x and 6 cancel out with the denominator, leaving us with $(6)4+(x)2=(6)5$ $24+2x=30$

Now, let’s solve it like any other equations. Subtract 24 from both sides. $2x=6$

Isolate the x and we have $x=3$ ## Video-Lesson Transcript

In this lesson, we’ll go over fractional equations.

This is just an equation involving fractions. But it’s algebra.

So, it’s going to be a little complicated.

For example: $\dfrac{4}{x} + \dfrac{2}{6} = \dfrac{5}{x}$

Let’s go back to the regular fractions for a second. Just a little side note. $\dfrac{1}{2} + \dfrac{1}{3}$

we need a common denominator.

We can’t just add it the way it is.

The common denominator for these is $6$.

In order to change the denominator by $6$, we have to multiply the numerator and the denominator by the same number.

In the first fraction, we have to multiply by $3$ and the second fraction has to be multiplied by $2$. $= \dfrac{3 \times 1}{3 \times 2} + \dfrac{1 \times 2}{3 \times 2}$ $= \dfrac{3}{6} + \dfrac{2}{6}$

We’re going to use the same concept in solving fractional equations.

First, we have to find the least common multiple of the denominators.

So our least common denominator (LCD) is $6x$.

But instead of getting the least common denominator and still having fractions, we’ll just multiply everything by the least common denominator.

If we multiply everything by $6x$, things are going to get canceled out.

And it’s not going to be a fractional equation anymore. It’s going to be regular equations. $\dfrac{4}{x} + \dfrac{2}{6} = \dfrac{5}{x}$ $(6x) \dfrac{4}{x} + (6x) \dfrac{2}{6} = (6x) \dfrac{5}{x}$

Now, we can cancel the denominators. $24 + 2x = 30$

Now, we can solve this like a regular equation.

We want to isolate $x$ using inverse operations. $24 - 24 + 2x = 30 - 24$ $2x = 6$ $\dfrac{2x}{2} = \dfrac{6}{2}$ $x = 3$
Then we end up with a new equation where we can solve for $x$.