  # Solve Each of the Following Quadratic Equations: a/(x-b)+b/(x-a)=2, x≠ b,a

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Updated on: October 17th, 2023 Solve each of the following quadratic equations: a/(x-b)+b/(x-a)=2,x≠b,a

To solve the quadratic equation a / (x – b)) + (b / (x – a) = 2, we can follow these steps:

Step 1: Multiply through by (x – b)(x – a) to eliminate the denominators.

Step 2: Expand and simplify the equation thus obtained. Then we will combine like terms

Step 3: On further solving, we will obtain two solutions for the equation.

Table of content ## Solve Each of the Following Quadratic Equations: a/(x-b)+b/(x-a)=2,x≠b,a

Solution:

Given the equation:

(a / (x – b)) + (b / (x – a)) = 2

To simplify the equation, we can find a common denominator:

[(a(x – a)) + (b(x – b))] / ((x – b)(x – a)) = 2

Expanding and simplifying the equation:

(ax – a² + bx – b²) = 2 ((x – b)(x – a))

(ax – a² + bx – b²) = 2x²–2ax–2bx+2ab

Rearranging the equation to bring all terms to one side:

2x² – 3x(a + b) + (a + b)² = 0

Expanding the middle term:

2x² – 2x(a + b)- x(a + b) + (a + b)² = 0

Combining like terms:

2x(x- (a + b)) – (a + b)(x- (a + b))= 0

Simplifying further:

(2x- (a + b))(x- (a + b))= 0

x = (a+b/2) and x = (a+b) GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com