Question

Solve the rational equation: 2x/x-4-2x-5/x^2-10x+24=-3/x-6

A. X=-0.64, x=1.44
B. There is no solution.
C. X=4, x=6
D. X=6.08, x=-0.58


Heellpppp plsss; timed test

Answer 1

D. X=6.08, x=-0.58

Explanation:

Given the rational expression

`(2x)/(x-4)-(2x-5)/(x^2-10x+24) = (-3)/(x-6)\\(2x)/(x-4)-(2x-5)/(x^2-4x-6x+24) = (-3)/(x-6)\\(2x)/(x-4)-(2x-5)/(x(x-4)-6(x-4)) = (-3)/(x-6)\\ \\(2x)/(x-4)-(2x-5)/((x-4)(x-6)) = (-3)/(x-6)\\Rerrange;\\(2x-5)/((x-4)(x-6)) = (2x)/(x-4)+ (3)/(x-6)\\(2x-5)/((x-4)(x-6)) = (2x(x-6)+3(x-4)))/((x-4)(x-6))\\`

Cancel out the denominator on both sides

`2x-5 = 2x(x-6)+3(x-4)\\Expand\\2x-5 =2x^2-12x+3x-12\\2x-5 = 2x^2-9x-12\\Equate \ to \ zero\\2x^2-9x-12-2x+5 = 0\\2x^2-11x - 7 = 0\\`

Factorize

`x = -(-11)\pm(√((-11)^2-4(2)(-7)) )/(2(2))\\x = 11\pm(√(121+56) )/(4)\\x = 11\pm(√(177) )/(4)\\x = 11\pm(13.3 )/(4)\\x = (11+13.3)/(4) \ and \ x = (11-13.3)/(4) \\x = 6.08 \ and \ - 0.58`

Hence the required solution is X=6.08 and -0.58