Algebra To Solve (a + 1 = 6/a)?

Question

I can solve simple equations like nobody's buisness, but the fraction bar has me thrown completely off. According to my teacher, I'd multiply by 1/a-1, but this only gets rid of part of the equation (and she's certianly been wrong before). Please help!

Answer 1

Take the equation,
a + 1 = 6/a
Multiply through by a
a^2 + a = 6
Subtract 6 from each side
a^2 + a - 6 = 0
Now you can factor
(a + 3)(a-2) = 0

So the solutions are a=-3, and a=2

Answer 2

forget the -1 for the moment
you put the 1 on the wrong side of the divisor multiply 6/a by a/1 the a's cancel each other out because the make an equal expression of 1 leaving 6/1 or just plain 6. balance the equation by multiplying a on the other side you should now have a^2 + 1 = 6

subtract 1 from both sides you get a^2 = 5 so the square root of 5 = a

Answer 3

a + 1 = 6 / a
=> a ( a + 1 ) = 6
=> a*a + a - 6 = 0
=> (a + 3 ) ( a -2) = 0

Therefore: a = -3 or a = 2

Answer 4

a + 1 = 6/a = (a+1)/1 = 6/a
a^2 + a = 6
a^2 + a - 6 = 0
(a+3)(a-2) = 0
a+3 = 0; a=-3
a-2 = 0; a=2

Answer: a= -3, 2

Answer 5

multiply by a
a(squared) + a - 6 = 0

then factor

(a + 3)(a - 2)

use the zero-product property

a + 3 = 0; a - 2 = 0

a = -3; a=2

Answer 6

a + 1 = 6/a multiply both sides by a
a^2+a=6 subtract 6 from both sides
a^2+a-6=0 factor
(a+3)(a-2)=0
a+3=0
a=-3
a=2=0
a=2

roots are a=2, -3

Answer 7

a + 1 = 6/a
a(a + 1) = 6
a^2 + a = 6
a^2 + a - 6 = 0
(a+3) (a-2) = 0

* a + 3 = 0 ==> a = -3
* a - 2 = 0 ==> a = 2

The answer: -3 and 2

Answer 8

a+1=6/a
multiplying by a
a^2+a-6=0
(a+3)(a-2)=0
a+3=0 or a=-3
a-2=0 or a=2

Answer 9

solve for zero and use the quadratic formula...
x=-3, 2