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Solve the equation : (5)/(2-x)+(x-5)/(...

Solve the equation :
`(5)/(2-x)+(x-5)/(x+2)+(3x+8)/(x^(2)-4)=0`

Text Solution

Verified by Experts

We have,
`(5)/(2-x)+(x-5)/(x+2)+(3x+8)/(x^(2)-4)=0`
`implies(5(x+2)+(2-x)(x-5))/((2-x)(x+2))-(3x+8)/((2+x)(2-x))=0`
`implies(5x+10+2x-10-x^(2)+5x-3x-8)/((2-x)(2+x))=0`
`implies-x^(2)+9x-8=0impliesx^(2)-9x+8=0`
`implies(x-1)(x-8)=0`
`:.x=1orx=8`
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