How do you subtract #\frac { 4} { 2r ^ { 4} s ^ { 5} } - \frac { 5} { 9r ^ { 3} s ^ { 7} }#?

Question

Julia Adams · Accepted Answer

#color(purple)(=>(18s^2 - 5r) / (9r^4s^7)# First let's find the L C M or L C D of #2r^4s^5 , 9 r^3 s^7# #L C M = 2 * 9 * r^4 * s ^ 7# #4 / (2r^4s^5) - 5 / (9 r^3 s^7) = (4 * 9 * s^2 - 5 * 2 * r)/ (18 r^4s^7)# #=> (36s^2 - 10r) / (18r^4s^7)# #=> (cancel2 * (18s^2 - 5r)) / (cancel2 * 9 r^4s^7# #color(purple)(=>(18s^2 - 5r) / (9r^4s^7)#

Hazel Anglin · Answer

undefined To subtract the given fractions, we need to find a common denominator. The common denominator for the fractions $\frac{4}{2r^4s^5}$ and $\frac{5}{9r^3s^7}$ is $18r^4s^7$.

Next, we multiply the numerator and denominator of each fraction by the appropriate factor to obtain the common denominator.

For the first fraction, we multiply the numerator and denominator by $9r^3s^2$ to get $\frac{36r^3s^2}{18r^4s^7}$.

For the second fraction, we multiply the numerator and denominator by $2r$ to get $\frac{10r}{18r^4s^7}$.

Now, we can subtract the fractions by subtracting their numerators while keeping the common denominator:

$\frac{36r^3s^2}{18r^4s^7} - \frac{10r}{18r^4s^7} = \frac{36r^3s^2 - 10r}{18r^4s^7}$.

Therefore, the subtraction of $\frac{4}{2r^4s^5} - \frac{5}{9r^3s^7}$ simplifies to $\frac{36r^3s^2 - 10r}{18r^4s^7}$.