We have the expression [tex] \frac{1}{y- \frac{1}{4} } [/tex]. To write a equivalent expression, we are going to rewrite the denominator of our expression using its common denominator 4:
[tex]\frac{1}{y- \frac{1}{4} } = \frac{1}{ \frac{4y-1}{4} } [/tex]
Now, notice that we are basically diving 1 by [tex] \frac{4y-1}{4} [/tex], so we have a division involving fractions, and remember that to divide fractions, we just need to invert the second fraction and multiply:
[tex] \frac{1}{ \frac{4y-1}{4} } =1* \frac{4}{4y-1} = \frac{4}{4y-1} [/tex]
We can conclude that the equivalent expression of [tex] \frac{1}{y- \frac{1}{4} } [/tex] is [tex] \frac{4}{4y-1} [/tex].
