Answer:
The equation without fraction would be: [tex]5x^2+x-6=0[/tex]
Step-by-step explanation:
Considering the equation
[tex]\frac{x^2+x-6}{2}=\frac{2\left(x-6\right)}{5}[/tex]
Steps to simplifying
[tex]\frac{x^2+x-6}{2}=\frac{2\left(x-6\right)}{5}[/tex]
[tex]\mathrm{Find\:Least\:Common\:Multiplier\:of\:}2,\:5:\quad 10[/tex]
[tex]\mathrm{Multiply\:by\:LCM=}10[/tex]
[tex]\frac{x^2+x-6}{2}\cdot \:10=\frac{2\left(x-6\right)}{5}\cdot \:10[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]5\left(x^2+x-6\right)=4\left(x-6\right)[/tex]
[tex]5x^2+5x-30=4x-24[/tex] ∵ [tex]\:5\left(x^2+x-6\right):\quad \:5x^2+5x-30[/tex] [tex]\mathrm{Add\:}24\mathrm{\:to\:both\:sides}[/tex]
[tex]5x^2+5x-30+24=4x-24+24[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]5x^2+5x-6=4x[/tex]
[tex]5x^2+x-6=0[/tex]
Therefore, the equation without fraction would be: [tex]5x^2+x-6=0[/tex]
Keywords: equation, fraction
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