Question

789/548x-89/887=688/8724 find x

Answer 1

$\frac{789}{548}x- \frac{89}{887}=\frac{688}{8724}$

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

$\frac{688}{8724}= \frac{688:4}{8724:4}=\frac{172}{2181}$

so:

$\frac{789}{548}x- \frac{89}{887}=\frac{172}{2181}$

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