Add fractions with exponents in the numerator How does one add these two terms with exponents in the numerator like h^2+(h^2)/4 ? According to my lesson on Khan Academy, one should get h^2(1+1/4). However, intuitively, it would seem that one would get (4h^2)/(4)+(h^2)/4 having first taken a common denominator and then 5 (h^2)/4. After having searched for clarification, none of the search results really helped me to derive the answer. Hopefully this will not add, as such, a redundant post. Please clarify.

Add fractions with exponents in the numerator
How does one add these two terms with exponents in the numerator like ${h}^{2}+\frac{{h}^{2}}{4}$?
According to my lesson on Khan Academy, one should get ${h}^{2}\left(1+\frac{1}{4}\right)$
However, intuitively, it would seem that one would get $\frac{4{h}^{2}}{4}+\frac{{h}^{2}}{4}$ having first taken a common denominator and then $5\frac{{h}^{2}}{4}$
After having searched for clarification, none of the search results really helped me to derive the answer. Hopefully this will not add, as such, a redundant post. Please clarify.
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efterynzl
note that
$\frac{{h}^{2}}{4}=\frac{1}{4}\cdot {h}^{2}$
thus we have
$\frac{4}{4}\cdot {h}^{2}+\frac{1}{4}\cdot {h}^{2}=\frac{5}{4}\cdot {h}^{2}$
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Logan Knox
${h}^{2}\left(1+\frac{1}{4}\right)$
You:
$5\frac{{h}^{2}}{4}=\frac{5}{4}{h}^{2}$
But
$1+\frac{1}{4}=\frac{4}{4}+\frac{1}{4}=\frac{5}{4}$
${h}^{2}\cdot \frac{5}{4}=\frac{5}{4}{h}^{2}$
which is the same as yours.