(1)/(2t-4)×(6+t-2t^(2))/(1-t)

Factor out common factor: Factor out the common factor in the denominator of the first fraction. The denominator 2t - 4 can be factored out as 2(t - 2). So, (1)/(2t-4) becomes (1)/(2(t-2)).Simplify expression: Simplify the expression by canceling out common factors if possible. We have (1)/(2(t-2))×(6+t-2t^(2))/(1-t). There are no common factors to cancel out between the numerators and denominators.Multiply numerators and denominators: Multiply the numerators and denominators of the two fractions. The numerator of the resulting fraction is (1)×(6+t-2t^(2)) = 6 + t - 2t^2. The denominator of the resulting fraction is (2(t-2))×(1-t) = 2(t-2)(1-t).Expand denominator: Expand the denominator. 2(t-2)(1-t) = 2(t - 2 - t^2 + 2t) = 2(-t^2 + 3t - 2).Write final expression: Write the final simplified expression. The final expression is (6 + t - 2t^2) / (2(-t^2 + 3t - 2)).

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Math Problems

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

\frac{1}{2 t-4} \times \frac{6+t-2 t^{2}}{1-t}

Factor out common factor: Factor out the common factor in the denominator of the first fraction. $\newline$ The denominator $2t - 4$ can be factored out as $2(t - 2)$ . $\newline$ So, $(1)/(2t-4)$ becomes $(1)/(2(t-2))$ .
Simplify expression: Simplify the expression by canceling out common factors if possible. $\newline$ We have $(\frac{1}{2(t-2)}\times\frac{6+t-2t^{2}}{1-t})$ . There are no common factors to cancel out between the numerators and denominators.
Multiply numerators and denominators: Multiply the numerators and denominators of the two fractions. $\newline$ The numerator of the resulting fraction is $(1)\times(6+t-2t^{2}) = 6 + t - 2t^2$ . $\newline$ The denominator of the resulting fraction is $(2(t-2))\times(1-t) = 2(t-2)(1-t)$ .
Expand denominator: Expand the denominator. $\newline$ $2(t-2)(1-t) = 2(t - 2 - t^2 + 2t) = 2(-t^2 + 3t - 2)$ .
Write final expression: Write the final simplified expression. $\newline$ The final expression is $(6 + t - 2t^2) / (2(-t^2 + 3t - 2))$ .