anonymous
  • anonymous
(1/x-1)+(1/x-12)=5/4
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
(1/x-1)+(1/x-12)=5/4 we multiply x-12/x-12 to (1/x-1) and x-1/x-1 to (1/x-12) this is possible since x-12/x-12 and x-1/x-1are both equal to 1 (1/x-1)(x-12/x-12) + (1/x-12)(x-1/x-1) = 5/4 (x-12/x-1*x-12) + (x-1/x-1*x-12) = 5/4 since the denominators are equal we add the numerators x-12+x-1/x-1*x-12=5/4 \[2x-13/x ^{2}-13x+12\] =5/4 then we cross multiply, 4(2x-13)=5(\[x ^{2}-13x+12\]) 8x-52 = \[5x ^{2}-65x+60\] \[5x ^{2}-65x+60\]-8x+52= 0 \[5x ^{2}-73x+112\] = 0 in a quadratic equation in the form \[ax ^{2}+bx+c=0\].\[(-b \pm \sqrt{b ^{2}-4ac})\div2a\] gives the two solutions of x. if you solve the formula the two solutions are 12.85 and 1.74 (you can try it out in a calculator) hope this helps

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