## ohhailayne 2 years ago 3/m-4+1/3(m-4)=6/m Help! Solving rational expressions

1. Linyu

$\frac{ 3 }{ m }-4+\frac{ 1 }{ 3(m-4) }=\frac{ 6 }{ m }$is it like this?

2. ohhailayne

yes! @Linyu I just need to know how to do it, my book doesn't give an example for ones like this

3. Linyu

you need to convert the denominators to the same form$\frac{ a }{ b }+\frac{ c }{ d }=\frac{ ad }{ bd }+\frac{ cb }{ bd }$

4. Linyu

@ohhailayne are you with me?

5. ohhailayne

7/m-4? @Linyu

6. Linyu

hmm... not sure if you catch up. Okay I'll try to solve this one step by step so you could understand

7. ohhailayne

10/m-4

8. ohhailayne

I think I've got it? @Linyu

9. Linyu

$\frac{ 3 }{ m }-\frac{ 4 }{ 1 }+\frac{ 1 }{ 3(m-4) }=\frac{ 6 }{ m }$ convert the denominator into 3m(m-4) we have$\frac{ 3(m-4) }{ 3(m-4) }\times \frac{ 3 }{ m }-\frac{ 3m(m-4) }{ 3m(m-4) }\times \frac{ 4 }{ 1 }+\frac{ m }{ m }\frac{ 1 }{ 3(m-4) }=\frac{ 3(m-4) }{ 3(m-4) }\times \frac{ 6 }{ m }$

10. Linyu

now all the denominators are the same 3m(m-4) so feel free to cancel them out. And you'll get$3(m-4)\times3-3m(m-4)\times4+m=3(m-4)\times6$

11. ohhailayne

the problem should be $\frac{ 3 }{ m-4 }+\frac{ 1 }{ 3(m-4) }=\frac{ 6 }{m? }$

12. Linyu

Oh! that will be better to solve

13. ohhailayne

yes! so I think the answer is 10/m-4 @Linyu

14. Linyu

3m(3)+m=3(m-4)(6) 9m+m=18m-72 10m=18m-72 0=8m-72 72=8m m=72/8 m=9

15. Linyu

the method is the same

16. ohhailayne

thanks @Linyu

17. Linyu

I hope you understand. Not only know the answer.