Perform the indicated operation and simplify the result. Leave your answer in factored form. [\frac{(4x-8)}{(-3x)} ]. [\frac{12}{(12-6x)}]

acomodats89m8

acomodats89m8

Answered question

2023-03-30

Perform the indicated operation and simplify the result. Leave your answer in factored form
[(4x8)(3x)].[12(126x)]

Answer & Explanation

pagarec0pz

pagarec0pz

Beginner2023-03-31Added 3 answers

To solve the given expression, we'll follow these steps:
Step 1: Simplify the expression inside the brackets.
Step 2: Multiply the two fractions together.
Step 3: Simplify the resulting expression.
Let's begin with step 1:
The expression inside the first bracket is 4x83x, and inside the second bracket is 12126x.
To simplify the first expression, we can factor out a common factor of 4 from the numerator:
4(x2)3x.
For the second expression, there are no common factors to factor out.
Now, let's move on to step 2:
To multiply the two fractions together, we multiply the numerators and the denominators:
4(x2)3x·12126x.
Multiplying the numerators gives us 4(x2)·12, and multiplying the denominators gives us 3x·(126x).
The expression now becomes:
4(x2)·123x·(126x).
Moving on to step 3:
Let's simplify the numerator first. Multiplying 4(x2)·12 gives us 48(x2).
Now, let's simplify the denominator. Multiplying 3x·(126x) can be done by distributing 3x into the parentheses:
3x·12+(3x)·(6x).
This simplifies to 36x+18x2.
The expression now becomes:
48(x2)36x+18x2.
To further simplify this expression, we can factor out a common factor of 6 from both the numerator and the denominator:
6·8(x2)6·(6x+3x2).
Simplifying, we have:
8(x2)6x+3x2.
Finally, we can factor out a common factor of 1 from the numerator to get:
8(x2)3x26x.
Now, let's factor out a common factor of x from the denominator:
8(x2)3x(x2).
Notice that the term (x2) appears in both the numerator and denominator. We can cancel out this common factor:
83x.
Therefore, the final simplified expression is:
83x.
But we can further simplify this by multiplying both the numerator and denominator by 1 to get the positive sign in the numerator:
83x.
Simplifying the negative signs, we have:
83x.
So, the final answer in factored form is:
83x.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?