Question

How do you solve the rational equation `a/(a+5) = 3/(a+1)`?

Answer 1

`a=-3, a=5`

Explanation:

`a/(a+5) = 3/(a+1)`

cross multiply:

`a(a+1) = 3(a+5)`

`a^2+a = 3a+15`

`a^2-2a -15= 0`
`(a+3)(a-5)= 0`

`a=-3, a=5`

Answer 2

`a=-3" or "a=5`

Explanation:

`"multiply through by "(a+5)(a+1)`

`cancel((a+5))(a+1)xxa/cancel(a+5)=(a+5)cancel((a+1))xx3/cancel(a+1)`

`a(a+1)=3(a+5)larrcolor(blue)"distribute"`

`a^2+a=3a+15`

`"rearrange in "color(blue)"standard form ";ax^2+bx+c=0`

`"subtract "3a+15" from both sides"`

`a^2-2a-15=0`

`"the factors of - 15 which sum to - 2 are - 5 and + 3"`

`(a-5)(a+3)=0`

`"equate each factor to zero and solve for a"`

`a+3=0rArra=-3`

`a-5=0rArra=5`