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Sagot :
Answer:
x = -1/2.
Step-by-step explanation:
x^2 - 4 = (x - 2)(x + 2) so if we multiply each term by x^2 -4 we get:
2 - 1(x - 2) = 3(x + 2)
2 - x + 2 = 3x + 6
2 + 2 - 6 = 3x + x
4x = -2
x = -1/2.
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
1. Multiply both sides of the equation by the LCM (x - 2)(x + 2):
[tex]\frac{2}{x^{2} -4} (x-2)(x+2)[/tex]
factor x² - 4 by rewriting it as x² - 2²
x² - 2² = (x + 2)(x - 2)
now we have;
[tex]\frac{2}{(x+2)(x-2)} (x-2)(x+2)[/tex]
cancel the common factors (x - 2)(x + 2)
= 2
-------------------------------
[tex]\frac{-1}{x+2} (x-2)(x+2)[/tex]
cross cancel the common factor (x + 2)
[tex]\frac{-1}{x-2}=-(x-2)=-x+2[/tex]
-------------------------------
[tex]\frac{3}{x-2} (x-2)(x+2)[/tex]
cross cancel the common factor (x - 2)
3(x + 2)
distribute the 3
3x + 6
-------------------------------
combining all new values, we have;
2 + (-x) + 2 = 3x + 6
-x + 4 = 3x + 6
2. Isolate x:
-x + 4-4 = 3x + 6-4
-x = 3x + 2
-x-3x = 3x-3x + 2
-4x = 2
-4x/-4 = 2/-4
x = [tex]-\frac{1}{2}[/tex]
hope this helps!
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