Question

Factories 5/x-5+2/x-2=3/x-3+4/x-4

Answer 1

Answer:

$\frac{5}{(x - 5)} + \frac{2}{(x - 2)} = \frac{3}{(x - 3)} + \frac{4}{(x - 4)} = >$

$\frac{ 5(x - 2) + 2(x - 5)}{(x - 2)(x - 5)} = \frac{3(x - 4) + 4(x - 3)}{(x - 3)(x - 4)} = >$

$\frac{7x - 20}{(x - 2)(x - 5)} = \frac{7x - 24}{(x - 3)(x - 4)} = >$

$(7x - 20)( {x}^{2} - 7x + 12) =$

$(7x - 24)( {x}^{2} - 7x + 10) = >$

$7 {x}^{3} - 49 {x}^{2} + 84x - 20 {x}^{2} + 140x -$

$240 = 7 {x}^{3} - 49 {x}^{2} + 70x - 24 {x}^{2} +$

$168x - 240 = >$

$4 {x}^{2} - 14x = 0 = > 2 {x}^{2} - 7x = 0 = >$

$x(2x - 7) = 0 = > x = 0 \: or \: \frac{7}{2}$

So

$x = 0 \: and \: \frac{7}{2} are \: solutions \: for \: the \:$

$following \: equatiom$