Clear of fractions and solve for x (x-3)/(x-1)=(x+1)/(x+2)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have (x-3)/(x-1)=(x+1)/(x+2), and we have to solve for x.

(x-3)/(x-1)=(x+1)/(x+2)

=> (x - 3)(x + 2) = (x + 1)(x - 1)

=> x^2 - x - 6 = x^2 - 1

=> -x = 5

=> x = -5

The required value of x = -5

aartihelpdesk's profile pic

aartihelpdesk | High School Teacher | (Level 1) Salutatorian

Posted on

Q: (x - 3) / (x - 1) = (x + 1) / (x + 2)

=>(x - 3) * (x + 2) = (x + 1) * (x - 1)

=>x^2 - 3x + 2x - 6 = x^2 - 1

=>    - 3x + 2x = 6 - 1

=>     x = - 5

Ans :-   minus 5  (-5)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll cross multiply and we'll get the cleared equation:

(x-1)(x+1) = (x-3)(x+2)

We notice that we'll get a difference of 2 squares to the left side. We'll remove the brackets from the right side:

x^2 - 1 = x^2 + 2x - 3x - 6

x^2 - 1 = x^2 - x - 6

We'll remove the like terms and we'll get:

-1 = -x - 6

We'll shift all terms to the left side:

x + 6 - 1 = 0

We'll combine like terms:

x + 5 = 0

x = -5

The solution of the equation is x = -5.

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