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Solve the Following Quadratic Equations by Factorization: `(2x)/(X-4)+(2x-5)/(X-3)=25/3` - Mathematics

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Question

Solve the following quadratic equations by factorization:

`(2x)/(x-4)+(2x-5)/(x-3)=25/3`

Solution

We have been given

`(2x)/(x-4)+(2x-5)/(x-3)=25/3`

`(2x(x-3)+(2x-5)(x-4))/(x^2-7x+12)=25/3`

6x2 - 18x + 6x2 - 24x - 15x + 60 = 25x2 - 175x + 300

13x2 - 118x + 240 = 0

13x2 - 78x - 40x + 240 = 0

13x(x - 6) - 40(x - 6) = 0

(x - 6)(13x - 40) = 0

Therefore,

x - 6 = 0

x = 6

or,

13x - 40 = 0

13x = 40

x = 40/13

Hence, x = 6 or x = 40/13

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.3 | Q: 23 | Page no. 20
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.3 | Q: 23 | Page no. 20
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Solution Solve the Following Quadratic Equations by Factorization: `(2x)/(X-4)+(2x-5)/(X-3)=25/3` Concept: Solutions of Quadratic Equations by Factorization.
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