## anonymous one year ago I WILL FAN AND MEDAL. What is the quotient in simplified form? State any restrictions on the variable. --> g-6 over g+2 / g+4 over g^2-g-6

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1. anonymous

@Abhisar @ganeshie8 @Nnesha Any help ? Didn't understand at all

2. anonymous

@pooja195 @nincompoop

3. Nnesha

$\huge\rm \frac{ \frac{ g- 6}{ g+2 } }{ \frac{ g+4 }{\color{red}{ g^2-g-6}} }$ like this ?

4. anonymous

nope, put the g+4 over g^2-g-6 at the right with the division sign in the middle @Nnesha

5. Nnesha

same thing :=)

6. Nnesha

$\huge\rm \frac{ \frac{ g- 6}{ g+2 } }{ \frac{ g+4 }{\color{red}{ g^2-g-6}} }=\frac{g-6}{g+2}\div\frac{g+4}{g^2-g+6}$

7. Nnesha

1st) try to factor out the equation g^2-g-6 how would you find factors of quadratic equation ?

8. anonymous

i dont know tbh @Nnesha

9. Nnesha

find two number when you multiply them you should get product of AC when you add or subtract the same two numbers you should get middle term a ,c and middle term is $\rm Ax^2+Bx+C$quadratic equation where a= leading coefficient b=middle term c=constant so what is a b and c in this equation g^2-g+6 ?

10. anonymous

a=1. b=1 and c=-6 ?

11. Nnesha

b=-1 b is negative so ac = -6 what two numbers you should multiply to get -6 but when you add them you should get -1

12. anonymous

-3 and 2

13. Nnesha

yes right so (g-3)(g+2) are factors of that equation $\huge\rm \frac{g-6}{g+2}\div\frac{g+4}{(g-3)(g+2)}$ now change division to multiplication multiply first fraction with the reciprocal of the 2nd fraction

14. Nnesha

i'll give u an example

15. Nnesha

$\huge\rm \frac{ a }{ b } \div \frac{ d }{ c }=\frac{ a }{ b } \times \frac{ c }{ d }$

16. anonymous

i give up i dont understand haha i just need the answer tbh

17. Nnesha

it's not that hard just flip the 2nd fraction and then change division sign to multiplication that's it

18. Nnesha

if i have 2/3 then its reciprocal would be 3/2