Processing Math: Done

From Förberedande kurs i matematik 1

Method 1

If we calculate the numerator in the main fraction first, we get

31041−51=3104515−5414=310520−420=310120.

The double fraction on the right-hand side becomes, after multiplying top and bottom by 103,

310120=120310310310=120310.

Then, we remove the common factor 10,

120310=1210310=123=61.

Method 2

Another way to calculate the expression is to divide it up into two separate terms

31041−51=41310−51310.

We simplify both double fractions on the right-hand side by multiplying top and bottom by 10/3

41310−51310=41310310310−51310310310=41310−51310.

Instead of multiplying, respectively, by 43 and 53, we keep the numerators factorized and observe that if we multiply the top and bottom of the first fraction by 5 and the second by 4, we obtain the common denominator

1043−1053=105435−104534=34550−40=10345.

Because 10=25 and 4=22, we can cancel out the common factors 2 and 5 and obtain the answer

10345=253225=132=61.