What is the answer to (2t+1)/(2t+3)=(3t-1)/(3t+4) ?

The answer to (2t+1)/(2t+3)=(3t-1)/(3t+4) is t=-7/4

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(2t+1)/(2t+3)=(3t-1)/(3t+4)

\frac{2 t + 1}{2 t + 3} = \frac{3 t - 1}{3 t + 4}

t = - \frac{7}{4}

Decimal Notation

t = - 1.75

Solution steps

\frac{2 t + 1}{2 t + 3} = \frac{3 t - 1}{3 t + 4}

Cross multiply

6 t^{2} + 11 t + 4 = 6 t^{2} + 7 t - 3

Move

4

to the right side

6 t^{2} + 11 t = 6 t^{2} + 7 t - 7

Subtract

6 t^{2} + 7 t

from both sides

6 t^{2} + 11 t - (6 t^{2} + 7 t) = 6 t^{2} + 7 t - 7 - (6 t^{2} + 7 t)

Simplify

4 t = - 7

Divide both sides by

4

t = - \frac{7}{4}

Verify Solutions

Find undefined (singularity) points:

t = - \frac{3}{2}, t = - \frac{4}{3}

Combine undefined points with solutions:

t = - \frac{7}{4}

\frac{4 x}{( 2 x + 2 ) + 6} = 24

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

\frac{2 x}{x ^{2} + 9} = 0

\frac{2}{x - 1} = \frac{x + 4}{3}

1 + \frac{3}{x - 1} = \frac{x + 5}{x ^{2} - 1}

What is the answer to (2t+1)/(2t+3)=(3t-1)/(3t+4) ?
The answer to (2t+1)/(2t+3)=(3t-1)/(3t+4) is t=-7/4
Solve for t: (2t+1)/(2t+3)=(3t-1)/(3t+4)
The solution is t=-7/4