How do you find the quotient of #8/(3x^2)div4/x#?

Question

Abigail Allen · Accepted Answer

#2/(3x)#

There are two ways to divide a fraction:

Method 1 Flip the second fraction, multiply, and simplify. #8/(3x^2) div 4/x = 8/(3x^2) xx x/4# #= (8x)/(12x^2) = 2/(3x)# Final Answer ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Method 2 Divide across without flipping. This method is not usually used, since it often results in a fraction over another fraction, which only makes things even harder to simplify. However, it is a perfectly valid method of division and, in the right cases, is much faster. #8/(3x^2) div 4/x = (8 div 4)/(3x^2 div x) = 2/(3x)# Final Answer

Abigail Allen · Answer

undefined To find the quotient of 8/(3x^2) divided by 4/x, we can simplify the expression by multiplying the numerator and denominator by the reciprocal of the second fraction.

First, we multiply 8/(3x^2) by x/4, which gives us (8x)/(12x^3).

Next, we simplify the expression by canceling out common factors. In this case, we can cancel out a factor of 4 from the numerator and denominator, resulting in (2x)/(3x^3).

Therefore, the quotient of 8/(3x^2) divided by 4/x simplifies to (2x)/(3x^3).