Question

Solve for x:
$fraction numerator 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis end fraction plus fraction numerator 1 over denominator left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space equals 2 over 3 comma space straight x not equal to 1 comma 2 comma 3$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

fraction numerator 1 over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis end fraction plus fraction numerator 1 over denominator left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction equals 2 over 3 therefore fraction numerator left parenthesis straight x minus 3 right parenthesis plus left parenthesis straight x minus 1 right parenthesis over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space equals 2 over 3 therefore fraction numerator straight x minus 3 plus straight x minus 1 over denominator left parenthesis straight x squared minus 2 straight x minus straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space equals 2 over 3 therefore fraction numerator 2 straight x minus 4 over denominator left parenthesis straight x squared minus 3 straight x plus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis end fraction space equals space 2 over 3 therefore fraction numerator 2 straight x minus 4 over denominator straight x cubed minus 3 straight x squared minus 3 straight x squared plus 9 straight x plus 2 straight x minus 6 end fraction space equals 2 over 3 therefore space fraction numerator 2 straight x minus 4 over denominator straight x cubed minus 6 straight x squared plus 11 straight x minus 6 end fraction space equals 2 over 3 therefore 6 straight x minus 12 equals 12 straight x cubed minus 12 straight x squared plus 22 space straight x minus 12 therefore 2 straight x cubed minus 12 straight x squared plus 16 straight x equals 0 therefore 2 straight x left parenthesis straight x squared minus 6 straight x plus 8 right parenthesis space equals 0 therefore left parenthesis straight x squared minus 6 straight x plus 8 right parenthesis space equals 0 straight x squared minus 4 straight x minus 2 straight x plus 8 space equals 0 straight x left parenthesis straight x minus 4 right parenthesis minus 2 left parenthesis straight x minus 4 right parenthesis equals 0 therefore space left parenthesis straight x minus 4 right parenthesis left parenthesis straight x minus 2 right parenthesis space equals 0 straight x equals 4 space or space straight x equals 2

For Daily Free Study Material Join wiredfaculty

Quadratic Equations

Some More Questions From Quadratic Equations Chapter

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:
x² – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x² + x – 6 = 0

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Quadratic Equations

Solve for x:

Some More Questions From Quadratic Equations Chapter

Represent the following problem situations in the form of quadratic equations:The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:x2 – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:2x2 + x – 6 = 0

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Represent the following problem situations in the form of quadratic equations:
The product of two consecutive positive integers is 306. We need to find the integers.

Represent the following problem situations in the form of quadratic equations:
Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Find the roots of the following quadratic equations by factorisation method:
x² – 3x – 10 = 0

Find the roots of the following quadratic equations by factorisation method:
2x² + x – 6 = 0