This week we learned about rational expressions, and how to multiply and divide them. The rules for this are very similar to multiplying and dividing fractions.

Multiplying:

Here is an example:

\frac {2x}{10x} * \frac {4y}{3}

Just like a fraction multiply straight across:

\frac {8xy}{30x}

Reduce this to \frac {4y}{15}

You must also state the non-permissible values, which you never do for the final answer, just the original expression once fully factored, so for this they are x ≠ 0.

Dividing

For dividing just like fractions we will multiply by the reciprocal:

\frac {3y}{6xy} \frac {2x}{5}

(pretend there’s a division sign there it wont work ^^^)

\frac {3x}{6xy} * \frac {5}{2x}

 

\frac {15x}{12x^2y}

 

\frac {5}{4xy}

For non-permissible values we must do it for the numerator AND denominator of the reciprocated fraction as well as the denominator of the other one, so our non-permissible values are x ≠  0, y ≠ 0.