Question

Create three fractions by replacing the word ‘blank’ in each fraction with a variable or number. You can use the same value or three different replacement values. Explain all the work in simplifying your new addition problem. 3/blank + blank/a^2 - blank/a^3

Answer 1

lets make blank = 7
then denominators are
\[7, a^2, 7a^3\] so a "common denominator" would be
\[7a^3\]

Answer 2

then you would have
\[\frac{3}{7}\times \frac{a^3}{a^3}+\frac{7}{a^2}\times \frac{7a}{7a}-\frac{7}{a^3}\times \frac{7}{7}\]

Answer 3

now all the denominators are
\[7a^3\] so you can compute in the numerator and get
\[\frac{3a^3+49a-49}{7a^3}\] feel free to pick a number other than 7
if you pick x you will get
\[\frac{3a^2+x^2a-x^2}{xa^3}\]