Marissa asked in Science & MathematicsMathematics · 2 months ago

# Can you simplify (8x-6)/(-4x+3)(x-2) any further?

Relevance
• 2 months ago

... ....8x - 6

=--------------------

..( - 4x + 3)(x - 2)

....2(4x - 3)

=--------------------- cancel out 4x - 3

..- (4x - 3)(x - 2)

......... 2

=- ------------

.......x - 2

• sepia
Lv 7
2 months ago

(8x - 6)/(-4x + 3)(x - 2)

= 2(4x - 3)/(4x - 3)(2 - x)

= 2/(2 - x)

• Pope
Lv 7
2 months ago

(8x - 6)/(-4x + 3)(x - 2)

= (8x - 6)(x - 2)/(-4x + 3)

= -2(-4x + 3)(x - 2)/(-4x + 3)

= -2(x - 2) ... x ≠ 3/4

= 4 - 2x ... x ≠ 3/4

There may be another order-of-operations issue here, but I am taking you at your word. If you meant something else, I will let you deal with it.

A more important point here concerns the removable discontinuity. That is an unfortunate expression, because many interpret it as meaning we can remove it and forget about it. We cannot. The given expression is undefined at x = 3/4. No amount of simplification can change that.

• 2 months ago

Yes you can.

(8x - 6) / (-4x + 3)(x - 2)

= -2(-4x + 3) / (-4x + 3)(x - 2)

= -2 / (x - 2).

• 2 months ago

As written:

(8x - 6) / (-4x + 3)(x - 2)

The (x - 2) is multiplied by the previous quotient.  So this is the same as:

(8x - 6)(x - 2) / (-4x + 3)

Now we can factor out the 2 from (8x - 6) and the -1 from the (-4x + 3) to get:

2(4x - 3)(x - 2) / [-(4x - 3)]

the (4x - 3)'s cancel out:

2(x - 2) / (-1)

And we can apply the -1 to the numerator to get:

-2(x - 2)

and simplify:

-2x + 4

---------------

If you meant the (x - 2) to be in the denominator, then the problem should be written as:

(8x - 6) / [(-4x + 3)(x - 2)]

Which then we can do the same factoring as before:

2(4x - 3) / [-(4x - 3)(x - 2)]

Cancel the (4x - 3):

2 / [-(x - 2)]

And apply the -1 to the numerator:

-2 / (x - 2)

It depends on what you really meant.  That's why the proper use of parenthesis is important.