Solve the rational equation. $$\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 1$$
A) $\{ 2 \}$
B) $\left\{ - \frac { 3 } { 2 } , 2 \right\}$
C) $\left\{ - 2 , \frac { 3 } { 2 } \right\}$
D) \{ \}

Question

Quizplus · Accepted Answer

To solve the equation $\frac{t^2}{3} - \frac{t}{6} = 1$, first find a common denominator to combine the fractions on the left side. The common denominator is 6, so multiply the entire equation by 6 to clear the fractions: $2t^2 - t = 6$. Rearrange the equation to set it to 0: $2t^2 - t - 6 = 0$. Factor the quadratic equation: $(2t + 3)(t - 2) = 0$. Set each factor equal to zero: $2t + 3 = 0$ and $t - 2 = 0$. Solve for $t$: $t = -\frac{3}{2}$ and $t = 2$. Therefore, the solution set is $\left\{ -\frac{3}{2}, 2 \right\}$.

Solve the Rational Equation t23−t6=1\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 13t2​−6t​=1

Solve the Rational Equation $\frac { t ^ { 2 } } { 3 } - \frac { t } { 6 } = 1$