Question(1) $\frac{4 x-1}{6}+\frac{4 x-5}{3}$

Studdy Solution

STEP 1

What is this asking? We're asked to simplify this expression by adding two fractions with $x$ in them! Watch out! Don't forget about those pesky common denominators when adding fractions.
Also, keep an eye on your signs – it's easy to make a mistake there.

STEP 2

1. Find a Common Denominator
2. Add the Fractions
3. Simplify

STEP 3

Alright, let's get this party started!
We've got two fractions here, and we need to find a common denominator before we can add them.
Notice that $6$ is a multiple of $3$ , since $2 \cdot 3 = 6$ .
So, our common denominator will be $6$ !

STEP 4

The first fraction already has a denominator of $6$ , so we're good there!
But the second fraction has a denominator of $3$ .
To get a denominator of $6$ , we need to multiply the top and bottom of the second fraction by $2$ .
Remember, multiplying by $\frac{2}{2}$ is the same as multiplying by $1$ , so it doesn't change the value of the fraction, just how it looks!
$\frac{4x - 5}{3} \cdot \frac{2}{2} = \frac{2 \cdot (4x - 5)}{2 \cdot 3} = \frac{8x - 10}{6}$

STEP 5

Now that both fractions have the same denominator, we can add them up!
Just add the numerators together and keep the denominator the same.
$\frac{4x - 1}{6} + \frac{8x - 10}{6} = \frac{(4x - 1) + (8x - 10)}{6}$

STEP 6

Let's combine like terms in the numerator.
We've got $4x$ and $8x$ , which add up to $12x$ .
And we've got $-1$ and $-10$ , which add up to $-11$ .
$\frac{4x + 8x - 1 - 10}{6} = \frac{12x - 11}{6}$

STEP 7

Now, let's see if we can simplify this fraction any further.
Can we divide both $12$ and $-11$ by a common factor that also divides $6$ ?
Well, $12$ and $6$ are both divisible by $6$ , but $11$ isn't divisible by anything other than $1$ and itself.
Since there are no common factors between $12$ , $-11$ , and $6$ (other than $1$ ), our fraction is already in its simplest form!

STEP 8

Our final answer is $\frac{12x - 11}{6}$ !
We rocked it!

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms