Question

a) Stiind ca a/b = 2/3, calculati 3a-b/a+b.
b) Stiind ca 5a-2b/2a+b=1/4, calculati a/b.
P.S. : "/" inseamna supra

Answer 1

$\frac{5a-2b}{2a+b}$ = $\frac{1}{4}$
4(5a-2b) = 1(2a+b)
20a - 8b = 2a+b
20a - 2a = b+8b
18a = 9b
$\frac{a}{b}$ = $\frac{9}{18}$
$\frac{a}{b}$ = $\frac{1}{2}$

a)  a/3 = b/2 = k
     a/3 = k, a = 3k
     b/2 = k, b = 2k
3a-b / a+b = 3*3k - 2k / 3k+2k =
                     9k-2k / 5k =
                     7k/5k