How do you simplify #2/(x-2) div (x-1)/(4x - 8)#?

Question

Eli Assouline · Accepted Answer

# 8/(x-1) #

Begin by factorising 4x - 8 = 4(x - 2)

fraction now becomes

#2/(x-2) ÷ (x-1)/(4(x-2))#

division of algebraic fractions is exactly the same as for numeric fractions.

#rArr color(red)(|bar(ul(color(white)(a/a)color(black)( a/b ÷ c/d = a/bxxd/c)color(white)(a/a)|)))#

so #2/(x-2) ÷ (x-1)/(4(x-2)) = 2/(x-2) xx(4(x-2))/(x-1) #

and cancelling (x-2) gives

#2/(cancel(x-2)) xx( 4cancel((x-2)))/(x-1) = 8/(x-1) #

Savannah Anderson · Answer

undefined To simplify the expression 2/(x-2) divided by (x-1)/(4x - 8), we can multiply the first fraction by the reciprocal of the second fraction.

Reciprocal of (x-1)/(4x - 8) is (4x - 8)/(x-1).

So, the expression simplifies to: 2/(x-2) * (4x - 8)/(x-1).

Next, we can simplify further by canceling out common factors between the numerators and denominators.

The numerator of the first fraction, 2, can be factored as 2 * 1.

The denominator of the first fraction, (x-2), and the numerator of the second fraction, (4x - 8), both have a common factor of 4.

The denominator of the second fraction, (x-1), and the numerator of the first fraction, 2, both have a common factor of 2.

After canceling out these common factors, the expression simplifies to:

(2 * 1 * (4x - 8))/(1 * 2 * (x-1)).

Simplifying further, we get:

(4x - 8)/(x-1).