Simplify: (x/y)/(b+y)/(y)

Question

(A) (b+y)/(x)

(B) (y)/x(b+y)

(C) (y)/(b+x)

(D) (x)/(by+1)

(E) None of these

Answer 1

When dividing fractions, we keep the top fraction, flip the bottom fraction over (invert it), and switch operations from division to multiplication. There are several little sayings to help remember this, one being "keep it, switch it, flip it" but the bottom line is that it becomes this problem:

From here, you can "cancel" the "y" on the upper right with the "y" on the lower left because y/y = 1 so the answer becomes x/(b + y)

Answer 2

Hi Jesset,

Based on what you've wrote this is the best way to do this is to write it all out:

You can simplify the fractions on the right by changing it to a fraction and multiplying by the reciprocal.

(x/y) * (y/(b+y))

Simplify it even further by canceling out the y in the numerator and denominator:

Therefore:

x / ( b+y)

is your solution.

Answer 3

See my comment on ambiguity...

(x/y)/(b+y)/(y) can be interpreted to mean:

((x/y) / (b+y)) / y

In that case, we have x / ((y^2)(b+y))