Fractions: Am I correct or is it incorrect?

Question

I wanted to know whether I did this math problem correct; if you could please let me know if I am incorrect or not I would greatly appreciate it! Thanks!

Perform the indicated operation and simplify.

5 + (t / t+2) - (8 / t^2-4)

i arrived at the answer of: 6t-14 / t-2

Thanks again!

Answer 1

5 + (t / t + 2) - (8 / t^2 - 4)

= 5 + [t / (t + 2)] - [8 / (t + 2)(t - 2)]

Get a common denominator of (t + 2)(t - 2)

= [5(t + 2)(t - 2) / (t + 2)(t - 2)] + [t(t - 2) / (t + 2)(t - 2)] - [8 / (t + 2)(t - 2)

With a common denominator in place, we can add the numerators

= [5(t + 2)(t - 2) + t(t - 2) - 8] / (t + 2)(t - 2)

Distribute the numerator

= [5(t^2 - 4) + t^2 - 2t - 8] / (t + 2)(t - 2)

= [5t^2 - 20 + t^2 - 2t - 8] / (t + 2)(t - 2)

Combine like terms in the numerator

= [6t^2 - 2t - 28] / (t + 2)(t - 2)

Factor out a 2 in the numerator

= 2(3t^2 - t - 14) / (t + 2)(t - 2)

Factor the numerator

= 2(3t - 7)(t + 2) / (t + 2)(t - 2)

Cancel the (t + 2)'s

= 2(3t - 7) / (t - 2)

You got it right!  You just need to factor a 2 from the numerator (real small thing).

Hope this helps you!  Please email anytime for further questions.

Answer 2

Yes, it's right, but put parentheses around it when you type...

(6t - 14)/(t - 2)

Take care,

David

Answer 3

I would say almost....( 6t -14) / ( t -2)  , t ╪ -2

Answer 4

Hi,

5 + (t / t+2) - (8 / t^2-4) =

....... ..t.. ......8

5.+.--------.-.-------- =

......t + 2....t² - 4

....... ..t.. ......8

5.+.--------.-.------------- =

......t + 2....(t-2)(t+2)

Get a common denominator of (t-2)(t+2) on each term. Then add fractions.

5(t-2)(t+2)....t(t-2).. ......8

--------------.+.-----------.-.-------... =

(t-2)(t+2)....(t-2)(t+2). .(t-2)(t+2)

5(t² -4).... ....t² -2t.. ......8

--------------.+.-----------.-.-------... =

(t-2)(t+2)....(t-2)(t+2). .(t-2)(t+2)

5(t² -4).+ t² -2t - 8

-------------------------- =

(t-2)(t+2)

5t² - 20.+ t² -2t - 8

-------------------------- =

(t-2)(t+2)

6t² - 2t - 28

----------------- =

(t-2)(t+2)

2(3t² - t - 14)

------------------ =

(t-2)(t+2)

2(3t - 7)(t + 2)

-------------------- =

(t-2)(t+2)

2(3t - 7)

------------ =

(t-2)

6t - 14

---------- <==ANSWER

t - 2

You are 100% correct!!

I hope that helps!! :-)