How do you simplify #(2x) /( x + 4) div (6)/(x-1)#?

Question

Abigail Allen · Accepted Answer

#(x(x-1))/(3(x+4))#

When we have a fraction divided by another fraction. Then leave the first fraction and multiply by the 'reciprocal' (flip the fraction over) of the second fraction.

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

#rArr(2x)/(x+4)÷6/(x-1)=(2x)/(x+4)xx(x-1)/6#

Now that we have multiplication we can cancel any factors on the numerators with any common factors on the denominators.

#rArr(cancel(2)^1 x)/(x+4)xx(x-1)/cancel(6)^3=x/(x+4)xx(x-1)/3#

We can now rewrite the product of these fractions as a single fraction.

In general : #color(red)(|bar(ul(color(white)(a/a)color(black)(a/b xxc/d=(ac)/(bd))color(white)(a/a)|)))#

#rArrx/(x+4)xx(x-1)/3=(x(x-1))/(3(x+4)#

Isaiah Anthony · Answer

undefined To simplify the expression (2x) / (x + 4) ÷ (6) / (x - 1), you can multiply the numerator and denominator of the first fraction by the reciprocal of the second fraction. This can be done as follows:

(2x) / (x + 4) ÷ (6) / (x - 1)
= (2x) / (x + 4) * (x - 1) / (6)
= (2x * (x - 1)) / ((x + 4) * 6)
= (2x^2 - 2x) / (6x + 24)
= (x^2 - x) / (3x + 12)

Therefore, the simplified expression is (x^2 - x) / (3x + 12).