Solving an equation with rational functions

[juliemariefort]

This is what I have done to solve this. Is it right?
t+5/t^2-3t-10 + 4/t-5 = 6/t+2

t+5/(t-5)(t+2) + 4/(t-5) = 6/(t+2)

t+ 5 + 4(t+2) = 6(t-5)

t + 5 + 4t + 8 = 6t -30

5t + 13 = 6t -30

t = 43

Thank you in advance for your help.

 

[wjm11]

This is what I have done to solve this. Is it right?
t+5/t^2-3t-10 + 4/t-5 = 6/t+2

t+5/(t-5)(t+2) + 4/(t-5) = 6/(t+2)

t+ 5 + 4(t+2) = 6(t-5)

t + 5 + 4t + 8 = 6t -30

5t + 13 = 6t -30

t = 43

Thank you in advance for your help.

Looks good, JulieMarie! For future reference, how would you check this yourself? The answer is to simply "plug in" your result into the original equation and see if it works.

Also note that whenever you have a variable in the denominator, make sure your answer does not make the denominator equal zero. Results that make the denominator equal zero are no good and are called "extraneous solutions."