What is the difference?
(r+2 / r+4) – (3 / r + 1)
(r+2)/(r+4) - 3/(r+1) = (r^2-10)/(r^2+5r+4)
Thank you
Well, the difference is that one expression involves math, while the other involves confusion and frustration. But fear not, I am here to help!
To simplify your expression, we need to find a common denominator. The common denominator of (r+4) and (r+1) is (r+4)(r+1). So, let's rewrite the expression using this common denominator:
((r+2)(r+1) - 3(r+4)) / (r+4)(r+1)
We can now distribute and simplify the numerator:
(r^2 + 3r + 2 - 3r - 12) / (r+4)(r+1)
The 3r terms cancel out, and we're left with:
(r^2 - 10) / (r+4)(r+1)
And there you have it! The difference between the two expressions is the simplified form of (r^2 - 10) / (r+4)(r+1). Voilà!
To find the difference between the expressions (r+2)/(r+4) and 3/(r+1), we need to subtract the second expression from the first. Follow the steps below:
Step 1: Determine the common denominator.
To combine the fractions, we need to find the least common denominator (LCD) of (r+4) and (r+1).
The LCD is (r+4)(r+1), since it is the smallest expression that both (r+4) and (r+1) divide into.
Step 2: Rewrite the fractions with the common denominator.
Now, we need to rewrite both fractions with the common denominator (r+4)(r+1).
For the first fraction (r+2)/(r+4), we need to multiply the numerator and denominator by (r+1) to obtain the common denominator:
(r+2)(r+1)/[(r+4)(r+1)]
For the second fraction 3/(r+1), we already have the common denominator.
So, the expression becomes:
[(r+2)(r+1)/[(r+4)(r+1)]] - [3/(r+1)]
Step 3: Simplify the expression.
Now that we have the fractions with the common denominator, we can subtract them:
[(r^2 + 3r + 2)/[(r+4)(r+1)]] - [3/(r+1)]
To subtract, we need a common denominator:
[(r^2 + 3r + 2) - (3(r+4))] / [(r+4)(r+1)]
Simplifying further, we have:
[(r^2 + 3r + 2) - (3r + 12)] / [(r+4)(r+1)]
[r^2 + 3r + 2 - 3r - 12] / [(r+4)(r+1)]
[r^2 - 10] / [(r+4)(r+1)]
Therefore, the difference between the expressions (r+2)/(r+4) and 3/(r+1) is (r^2 - 10) / [(r+4)(r+1)].
To find the difference between two fractions, we need to find a common denominator and then subtract the numerator of one fraction from the numerator of the other.
Let's start by finding the common denominator for the two fractions: (r+4) and (r+1). Since both denominators are already in factored form, we can directly multiply them together to get the common denominator.
Common denominator = (r+4) * (r+1)
Now, let's simplify the expression:
(r+2) / (r+4) - 3 / (r+1)
To make the denominators the same, we need to multiply the first fraction by (r+1) and the second fraction by (r+4). This way, the denominators will become (r+4) * (r+1) for both fractions.
Next, we apply the distributive property to multiply the numerators:
[(r+2) * (r+1)] / [(r+4) * (r+1)] - (3 * (r+4)) / [(r+1) * (r+4)]
Now, let's simplify the expression further:
[(r^2 + 3r + 2) / [(r+4) * (r+1)] - (3r + 12) / [(r+1) * (r+4)]
The denominators are now the same, so we can subtract the numerators:
[(r^2 + 3r + 2) - (3r + 12)] / [(r+4) * (r+1)]
Simplifying the numerator:
[r^2 + 3r + 2 - 3r - 12] / [(r+4) * (r+1)]
[r^2 - 10] / [(r+4) * (r+1)]
Therefore, the difference is (r^2 - 10) / [(r+4) * (r+1)].