Given:
The expression is .
To find:
The shows the correct way to use the rule ""multiply by the reciprocal"" for the given expression.
Solution:
According to the rule "multiply by the reciprocal", if a,b,c,d are four number, then
We have,
It can be written as
Using the rule "multiply by the reciprocal", we get
Therefore, the correct option is D.
first we try to semplify as much as possible the fractions.
First we decompose the numbers
789 = 3 * 263
548 = 2 * 2 * 137 = 2^2
they have nothing in common, so the first fraction remains so
89 = 89 (prime number)
887 = 887 (prime number)
they have nothing in common, so the second one remains so
688 = 2 * 2 * 2 * 2 * 43 = 2^4 * 43
8724 = 2 * 2 * 3 * 727 = 2^2 * 3 * 727
they have 2^2 (=4) in common, so the numerator and the denominator can be devided by 4
so:
now we calculate the common denominator
take the scomposition:
548 = 2^2 * 137
887 = 887
2181 = 3 * 727
take every number one time
so the common denominator is 2^2 * 137 * 887 * 727 * 3 = 1'060'131'756
now calculate every single numerator: first we divide each denominator by the common denominator, then we moltiply the result with each numerator
first fraction: 789/548
1060131756 / 548 = 1934547
1934547 * 789 = 1526357583
second fraction: 89/887
1060131756 / 887 = 1195188
1195188 * 89 = 106371732
third one: 172/2181
1060131756 / 2181 = 486076
486076 * 172 = 83605072
now we can delete the common denominator
1526357583x - 106371732 = 83605072
solve it
1526357583x = 83605072 + 106371732
1526357583x = 189976804
x = 1526357583 / 189976804
decompose
1526357583 = 887 * 3 * 3 * 727 * 263
189976804 = 137 * 2 * 2 * 211 * 53 * 31
nothing in common
x = 1526357583 / 189976804