### (x+1)/(x+4)=(2x-1)/(x+6)

(x + 1)(x+6) = (2x - 1)(x+4) x both sides by (x + 4)(x + 6)

x^2 + 7x + 6 = 2x^2 + 7x - 4 Expand the parenthesis

x^2 + 6 = 2x^2 - 4 Subtract 7x from both sides

10 = x^2 Add (4 - x^2) to both sides

+- sqrt(10) = x Take square root of both sides

(x+1)/(x+4)=(2x-1)/(x+6)

cross multiply the numbers

(x+1)(x+6) = (x+4)(2x-1)

unfoil the problem by multiplying every number from the first parenthesis by the numbers inside the second parenthesis

you should end up with

`x^2 +7x + 6 = 2x^2 + 7x - 4 `

Add the opposite of each number to combine like terms

x^2 +7x + 6 = 2x^2 + 7x - 4

+4 +4

x^2 +7x + 10 = 2x^2 + 7x

-7x -7x

x^2 + 10 = 2x^2

-x^2 -x^2

`10=x^2 `

find the square root

`sqrt(10) =sqrt(x^2)`

`x= +-sqrt(10)`

`(x+1)/(x+4)=(2x-1)/(x+6)`

Cross multiply:

(x+1)(x+6) = (x+4)(2x-1)

FOIL both sides

x^2 +7x + 6 = 2x^2 + 7x - 4

Bring all terms to one side

x^2 - 10 = 0

x^2 = 10

x = plus or minus sqrt(10)

We'll use the property of equal ratios, so we'll subtract the denominator from numerator, at both sides of the equality:

(x+1-x-4)/(x+4)=(2x-1-x-6)/(x+6)

-3/(x+4)=(x-7)/(x+6)

We'll cross multiplying and the result will be:

-3*(x+6)=x^2-3*x-28

We'll reduce the similar terms, both sides of the equality,

"-3x"

-18=x^2-28

x^2-10=0

x^2=10

x1=+ sqrt 10

x2=- sqrt 10

Multiply both sides of the given expression by the LCM (x+6) (x+4) to get rid of the denominator. Then we get:

(x+1)(x+6) =(2x-1)(x+4)

Expand both sides :

x^2+6x+x+6 =2x^2+8x-x-4

Simplify both sides:

x^2+7x+6=2x^2+7x-4.

Subtract x^2+7x+6 from both sides:

0=2x^2+7x-4-(x^2+7x+6)

0=x^2-10

x^2 = 10 or

**x= + sqrt(10) **or **x=-sqrt(10)**