Question

Solve each proportion

Answer 1

`(11)/(b - 1) = (6)/(b + 1) \\ 11(b + 1) = (b - 1).6 \\ 11b + 11 = 6b - 6 \\ 11b + 11 - 11 = 6b - 6 - 11 \\ 11b - 6b = 6b - 17 - 6b \\ 5b = - 17 \\ (5b)/(5) = ( - 17)/(5) \\ b = ( - 17)/(5) \\ b = - 3.4`

Answer 2

`\boxed{\underline{\bf \: Answer}}`

`\sf (11)/(b + 1) = (6)/(b + 1) \\`

Multiply both sides of the equation by
`\left(b-1\right)\left(b+1\right)`, the least common multiple of b-1,b+1.

`\sf\left(b+1\right)* 11=\left(b-1\right)* 6`

Use the distributive property to multiply b+1 by 11.

`\sf11b+11=\left(b-1\right)* 6`

Subtract 6b from both sides.

`\sf11b+11-6b=-6`

Combine 11b and -6b to get 5b.

`\sf5b+11=-6`

Subtract 11 from both sides.

`\sf5b=-6-11`

Subtract 11 from -6 to get -17.

`\sf5b=-17`

Divide both sides by 5.

`\sf \: b=\bf(-17)/(5)`

=> The correct answer is
`\bf \: b=(-17)/(5)` or
`\bf \: b= -3.4` (✓).

__________

Hope it helps.

RainbowSalt2222