4/x-3=5/2x+3
solve using factorisation method
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Answer:
4/x-3=5/2x+3
=4/x-5/2x=6
3/2x=6
3=12x
x=4
Verified answer
GIVEN :
[tex] \frac{4}{x} - 3 = \frac{5}{2x + 3} [/tex]
TO FIND :
The value of X using factorisation method.
SOLUTION :
[tex]⟶ \frac{4}{x} - 3 = \frac{5}{2x + 3}[/tex]
[tex]⟶ \frac{(4 - 3x)}{x} = \frac{5}{2x + 3}[/tex]
Now cross multiply :-
[tex]⟶ (4 - 3x)(2x + 3) = 5x[/tex]
[tex]⟶ 8x + 12 - 6 {x}^{2} - 9x = 5x[/tex]
[tex]⟶ 8x + 12 - 6 {x}^{2} - 9x - 5x = 0 [/tex]
[tex]⟶ 12 - 6 {x}^{2} -6 x = 0[/tex]
taking out -6 as common we get =>
⟶ [tex] {x}^{2} + x - 2 = 0[/tex]
Now we will factorize by using middle term factorisation method :-
⟶ [tex]{x}^{2} + 2x - x - 2 = 0[/tex]
now taking out common=>
⟶ [tex]x(x + 2) - 1(x + 2) = 0[/tex]
taking out (x+2) as common ⟶
⟶ [tex](x - 1)(x + 2) = 0[/tex]
Therefore x = 1 or X = -2
ANSWER :
X = 1 or -2