What is the answer to 1/(3(t+6)-10)=-3t+2 ?

The answer to 1/(3(t+6)-10)=-3t+2 is t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3

Solve for t: 1/(3(t+6)-10)=-3t+2

The solution is t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3

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\frac{1}{3 ( t + 6 ) - 10} = - 3 t + 2

t = - \frac{3 + 2 6}{3}, t = \frac{2 6 - 3}{3}

Decimal Notation

t = - 2.63299 \dots, t = 0.63299 \dots

Solution steps

\frac{1}{3 ( t + 6 ) - 10} = - 3 t + 2

Simplify

\frac{1}{3 ( t + 6 ) - 10} : \frac{1}{3 t + 8}

\frac{1}{3 t + 8} = - 3 t + 2

Multiply both sides by

3 t + 8

1 = - 3 t (3 t + 8) + 2 (3 t + 8)

Solve

1 = - 3 t (3 t + 8) + 2 (3 t + 8) : t = - \frac{3 + 2 6}{3}, t = \frac{2 6 - 3}{3}

t = - \frac{3 + 2 6}{3}, t = \frac{2 6 - 3}{3}

Verify Solutions

Find undefined (singularity) points:

t = - \frac{8}{3}

Combine undefined points with solutions:

t = - \frac{3 + 2 6}{3}, t = \frac{2 6 - 3}{3}

\frac{6}{y - 3} - \frac{4}{y - 3} = 2

\frac{3}{x - 3} = 4 + \frac{x}{x - 3}

y, x = \frac{y - 5}{y - 2}

\frac{6}{x} + \frac{4}{x + 9} = 9

\frac{3 x - \frac{7}{2}}{2 x} = 5

What is the answer to 1/(3(t+6)-10)=-3t+2 ?
The answer to 1/(3(t+6)-10)=-3t+2 is t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3
Solve for t: 1/(3(t+6)-10)=-3t+2
The solution is t=-(3+2sqrt(6))/3 ,t=(2sqrt(6)-3)/3