Question 372650
{{{sqrt(5x-5)- sqrt(4x-3)=1}}}
{{{sqrt(5x-5)=sqrt(4x-3)+1}}}
Square both sides.
{{{5x-5=4x-3+2*sqrt(4x-3)+1}}}
{{{5x-5=4x-2+2*sqrt(4x-3)}}}
{{{x-3=2*sqrt(4x-3)}}}
Square both sides again.
{{{x^2-6x+9=4(4x-3)}}}
{{{x^2-6x+9=16x-12}}}
{{{x^2-22x+21=0}}}
{{{(x-21)(x-1)=0}}}
Two solutions:
{{{x-21=0}}}
{{{x=21}}}
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{{{x-1=0}}}
{{{x=1}}}
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Verify both solutions by plugging them back into the original equation.
Remember {{{sqrt(a^2)=0 +- a}}}.