Solve the rational equation: \(\displaystyle{\frac{{{x}-{2}}}{{{x}^{{2}}-{4}}}}+{\frac{{{1}}}{{{x}+{2}}}}={\frac{{{1}}}{{{x}-{2}}}}\)

brunocazelles4dvb

brunocazelles4dvb

Answered question

2022-03-21

Solve the rational equation:
x2x24+1x+2=1x2

Answer & Explanation

Janessa Foster

Janessa Foster

Beginner2022-03-22Added 12 answers

x2x24+1x+2=1x2
The least common denominator of x24, x+2, x2 is x24
Multiply both sides by LCD
(x24)[x2x24+1x+2]=(x24)1x2
Apply distribution property
(x24)x2x24+x24x+2=x24x2
[x24=(x+2)(x2)]
Now,
(x2)+(x2)=x+2
2x4=x+2
x=2+4
x=6
Now, substitute the value x=6 in the original equation
62624+16+2=162
4364+18=14
432+18=14
18+18=14
28=14
14=14

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