acomodats89m8

2023-03-30

Perform the indicated operation and simplify the result. Leave your answer in factored form

$\left[\frac{(4x-8)}{(-3x)}\right].\left[\frac{12}{(12-6x)}\right]$

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 $\frac{4x-8}{-3x}$, and inside the second bracket is $\frac{12}{12-6x}$.

To simplify the first expression, we can factor out a common factor of 4 from the numerator:

$\frac{4(x-2)}{-3x}$.

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:

$\frac{4(x-2)}{-3x}\xb7\frac{12}{12-6x}$.

Multiplying the numerators gives us $4(x-2)\xb712$, and multiplying the denominators gives us $-3x\xb7(12-6x)$.

The expression now becomes:

$\frac{4(x-2)\xb712}{-3x\xb7(12-6x)}$.

Moving on to step 3:

Let's simplify the numerator first. Multiplying $4(x-2)\xb712$ gives us $48(x-2)$.

Now, let's simplify the denominator. Multiplying $-3x\xb7(12-6x)$ can be done by distributing $-3x$ into the parentheses:

$-3x\xb712+(-3x)\xb7(-6x)$.

This simplifies to $-36x+18{x}^{2}$.

The expression now becomes:

$\frac{48(x-2)}{-36x+18{x}^{2}}$.

To further simplify this expression, we can factor out a common factor of 6 from both the numerator and the denominator:

$\frac{6\xb78(x-2)}{6\xb7(-6x+3{x}^{2})}$.

Simplifying, we have:

$\frac{8(x-2)}{-6x+3{x}^{2}}$.

Finally, we can factor out a common factor of $-1$ from the numerator to get:

$\frac{-8(x-2)}{3{x}^{2}-6x}$.

Now, let's factor out a common factor of $x$ from the denominator:

$\frac{-8(x-2)}{3x(x-2)}$.

Notice that the term $(x-2)$ appears in both the numerator and denominator. We can cancel out this common factor:

$\frac{-8}{3x}$.

Therefore, the final simplified expression is:

$\frac{8}{-3x}$.

But we can further simplify this by multiplying both the numerator and denominator by $-1$ to get the positive sign in the numerator:

$\frac{-8}{-3x}$.

Simplifying the negative signs, we have:

$\frac{8}{3x}$.

So, the final answer in factored form is:

$\frac{8}{3x}$.

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 $\frac{4x-8}{-3x}$, and inside the second bracket is $\frac{12}{12-6x}$.

To simplify the first expression, we can factor out a common factor of 4 from the numerator:

$\frac{4(x-2)}{-3x}$.

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:

$\frac{4(x-2)}{-3x}\xb7\frac{12}{12-6x}$.

Multiplying the numerators gives us $4(x-2)\xb712$, and multiplying the denominators gives us $-3x\xb7(12-6x)$.

The expression now becomes:

$\frac{4(x-2)\xb712}{-3x\xb7(12-6x)}$.

Moving on to step 3:

Let's simplify the numerator first. Multiplying $4(x-2)\xb712$ gives us $48(x-2)$.

Now, let's simplify the denominator. Multiplying $-3x\xb7(12-6x)$ can be done by distributing $-3x$ into the parentheses:

$-3x\xb712+(-3x)\xb7(-6x)$.

This simplifies to $-36x+18{x}^{2}$.

The expression now becomes:

$\frac{48(x-2)}{-36x+18{x}^{2}}$.

To further simplify this expression, we can factor out a common factor of 6 from both the numerator and the denominator:

$\frac{6\xb78(x-2)}{6\xb7(-6x+3{x}^{2})}$.

Simplifying, we have:

$\frac{8(x-2)}{-6x+3{x}^{2}}$.

Finally, we can factor out a common factor of $-1$ from the numerator to get:

$\frac{-8(x-2)}{3{x}^{2}-6x}$.

Now, let's factor out a common factor of $x$ from the denominator:

$\frac{-8(x-2)}{3x(x-2)}$.

Notice that the term $(x-2)$ appears in both the numerator and denominator. We can cancel out this common factor:

$\frac{-8}{3x}$.

Therefore, the final simplified expression is:

$\frac{8}{-3x}$.

But we can further simplify this by multiplying both the numerator and denominator by $-1$ to get the positive sign in the numerator:

$\frac{-8}{-3x}$.

Simplifying the negative signs, we have:

$\frac{8}{3x}$.

So, the final answer in factored form is:

$\frac{8}{3x}$.

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