The equation 1t−1+t3t−2=12 is either linear or equivalent to a linear equation. Solve the equation
1t−1+t3t−2=12Get the LCD of the left side3t−2+t(t−1)(t−1)(3t−2)=12Simplify3t−2+t2−t(t−1)(3t−2)=12Combine like termst2+2t−2(t−1)(3t−2)=12Factor the numerator\cancel(t−1)(t+2)\cancel(t−1)(3t−2)=12Cancel out like termst+23t−2=12Multiply both sides by 2(3t−2)2(\cancel3t−2)[t+2\cancel3t−2=1\cancel2]\cancel2(3t−2)Simplify2(t+2)=3t−2Apply Distributive property2t+4=3t−2Combine like terms2t−3t=−4−2Simplify−t=−6Multiply both sides by -1−1[−t=−6]−1Simplifyt=6
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