Answer:
[tex]\frac{15y-10}{15y-3}[/tex]
Step-by-step explanation:
First at all, we need to use [tex]a=\frac{a}{1}[/tex] to convert this expression into a fraction, like:
[tex]y-\frac{2}{3}[/tex] to convert into [tex]\frac{y}{1} -\frac{2}{3}[/tex].
Expand the fraction to get the least common denominator, like
[tex]\frac{3y}{3*1}-\frac{2}{3}[/tex]
Write all numerators above the common denominator, like this:
[tex]\frac{3y-2}{3}[/tex]
The bottom one used the same way to became simplest form, like this:
[tex]y+\frac{1}{5}[/tex]
[tex]\frac{y}{1} +\frac{1}{5}[/tex]
[tex]\frac{5y}{5*1}+\frac{1}{5}[/tex]
[tex]\frac{5y+1}{5}[/tex]
And it became like this:
[tex]\frac{3y-2}{3}/\frac{5y+1}{5}[/tex]
Now, we are going to simplify this complex fraction. We can use cross- multiply method to simplify this fraction.
[tex]\frac{3y-2}{3}*\frac{5y+1}{5}[/tex]
3y-2(5) and 5y-1(3)
and it will becomes like this in function form:
[tex]\frac{3y-2(5)}{5y+1(3)}[/tex]
Then, we should distribute 5 through the parenthesis
[tex]\frac{15y-10}{5y+1(3)}[/tex]
[tex]\frac{15y-10}{15y+3}[/tex]
And.... Here we go. That is the answer.
