SOLUTION: 4/(x-1)^2-12/(3x-1)^2=3

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Question 1152366: 4/(x-1)^2-12/(3x-1)^2=3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

4%2F%28x-1%29%5E2-12%2F%283x-1%29%5E2=3



%284%283x-1%29%5E2-12%28x-1%29%5E2%29%2F%28%283x-1%29%5E2%2A%28x-1%29%5E2%29=3

%284%283x-1%29%5E2-12%28x-1%29%5E2%29=3%28%283x-1%29%5E2%2A%28x-1%29%5E2%29

4%289x%5E2-6x%2B1%29-12%28x%5E2-2x%2B1%29=3%28%289x%5E2-6x%2B1%29%2A%28x%5E2-2x%2B1%29%29

36x%5E2+-+24x+%2B+4-%2812x%5E2+-+24x+%2B+12%29=27x%5E4+-+72x%5E3+%2B+66x%5E2+-+24x+%2B+3

36x%5E2+-+24x+%2B+4-12x%5E2+%2B24x+-12=27x%5E4+-+72x%5E3+%2B+66x%5E2+-+24x+%2B+3

24x%5E2+-+8=27x%5E4+-+72x%5E3+%2B+66x%5E2+-+24x+%2B+3

0=27x%5E4+-+72x%5E3+%2B+66x%5E2-24x%5E2++-+24x+%2B+3%2B8

27x%5E4+-+72x%5E3+%2B+42x%5E2+-+24x+%2B+11=0

%283x%5E2+%2B+1%29+%289x%5E2+-+24x+%2B+11%29+=+0


if %283x%5E2+%2B+1%29++=+0=>3x%5E2+=+-1 =>x%5E2+=+-1%2F3
=>x+=+sqrt%28-1%2F3%29
so,
solutions:x+=+i%2Fsqrt%283%29 or x+=+-i%2Fsqrt%283%29


if +9x%5E2+-+24x+%2B+11+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-24%29+%2B-+sqrt%28+%28-24%29%5E2-4%2A9%2A11+%29%29%2F%282%2A9%29+
x+=+%2824+%2B-+sqrt%28+576-396+%29%29%2F18+
x+=+%2824+%2B-+sqrt%28+180%29%29%2F18+
x+=+%2824+%2B-+sqrt%28+36%2A5%29%29%2F18+
x+=+%2824+%2B-+6sqrt%28+5%29%29%2F18+
x+=+%28cross%2824%294+%2B-+cross%286%29sqrt%28+5%29%29%2Fcross%2818%293+

x+=+%284+%2B-+sqrt%28+5%29%29%2F3+
solutions:
x+=+4%2F3+%2B+sqrt%285%29%2F3

x+=+4%2F3+-sqrt%285%29%2F3