Question 306418

{{{sqrt(x+1)-sqrt(4x-3)=1}}}
{{{(x+1)-2sqrt(x+1)sqrt(4x-3)+(4x-3)=1}}}
{{{x+1+4x-3-1=2sqrt((x+1)(4x-3))}}}
{{{5x-3=2sqrt((x+1)(4x-3))}}}
{{{(5x-3)^2=4(x+1)(4x-3)}}}
{{{25x^2-30x+9=4(4x^2+x-3)}}}
{{{25x^2-30x+9=16x^2+4x-12}}}
{{{9x^2-34x+21=0}}}
Factor.
{{{(9x-7)(x-3)=0}}}
Two solutions:
{{{9x-7=0}}}
{{{9x=7}}}
{{{x=7/9}}}
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{{{x-3=0}}}
{{{x=3}}}
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I leave it to you to verify that those are indeed solutions to the problem. 
Remember that {{{sqrt(a^2)=0 +- a}}}