No products in the cart.

Find the root of 2x-3/x-2+2x-7/x-4=16/3

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Find the root of 2x-3/x-2+2x-7/x-4=16/3
  • 1 answers

Rajan Kumar Pasi 4 years, 9 months ago

{tex}Question:\space\large{ {2x-3\over x-2} +{2x-7\over x-4} = {16\over 3}, find \space x?}{/tex}

{tex}\large {Solution:\\ } {/tex}

{tex}\large { \underline {Step\space 1:\space Fraction\space solving} } {/tex}

{tex}\large\implies {{\big((2x-3)(x-4)\big)} +{\big((2x-7)(x-2)\big)}\over {(x-2)(x-4)}} = {16\over 3}{/tex}

{tex}\large\implies {{\big((2x^2-8x-3x+12)\big)} +{\big((2x^2-4x-7x+14)\big)}\over {(x^2-4x-2x+8)}} = {16\over 3}{/tex}

{tex}\large\implies {{\big(2x^2-11x+12+2x^2-11x+14\big)}\over {(x^2-6x+8)}} = {16\over 3}{/tex}

{tex}\large\implies {{\big(4x^2-22x+26\big)}\over {(x^2-6x+8)}} = {16\over 3}{/tex}

{tex}\large{ \underline {Step\space 2:\space Cross-multiplication}\\\implies {{3\times \big (4x^2-22x+26\big)} } = {16\times {(x^2-6x+8)}}}{/tex}

 

{tex}\large{ \underline {Step\space 3:\space Simplification:}\\\implies {{\big (12x^2-66x+78\big)} } = {{(16x^2-96x+128)}}}{/tex}

 

{tex}\large {\underline {Step\space 4:\space Equation-solving:}\\\implies 16x^2-96x+128-12x^2+66x-78=0}{/tex}

{tex}\large {\underline {Step\space 5:\space Arranging\space like-terms:}\\\implies 16x^2-12x^2-96x+66x+128-78=0}{/tex}

{tex}\large{\\\implies 4x^2-30x+50=0}{/tex}

 

{tex}\large {\underline {Step\space 6:\space Taking\space out\space common-terms:}\\\implies 2\times (2x^2-15x+25)=0}{/tex}

{tex}\large {\\\implies 2x^2-15x+25=0}{/tex}

{tex}\large {\underline {Step\space 7:\space Middle-term\space splitting\space :}\\\implies 2x^2-10x-5x+25=0}{/tex}

{tex}\large{ \underline {Step\space 8:\space Grouping\space :}\\\implies 2x(x-5)-5(x-5)=0}{/tex}

{tex} \\\implies \large(2x-5)(x-5)=0{/tex}

{tex} \\\implies\huge \therefore \boxed{x=5\space or \space {5\over2}}{/tex}





 

http://mycbseguide.com/examin8/

Related Questions

Tc9fvyfi6ez
  • 0 answers
2x-3y=8 answer
  • 0 answers
[ ]/[ ] of 125 =100
  • 0 answers
X²-3x-4=0
  • 0 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Download myCBSEguide App