Solve the equation. sqrt(5x+1)-1=sqrt(3x)

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Isolate square root: Isolate one of the square roots. sqrt(5x+1) = sqrt(3x) + 1Square both sides: Square both sides to eliminate the square root on the left side. (sqrt(5x+1))^2 = (sqrt(3x) + 1)^2Apply squaring operation: Apply the squaring operation to both sides. 5x + 1 = (sqrt(3x))^2 + 2*sqrt(3x)*1 + 1^2Simplify right side: Simplify the right side of the equation. 5x + 1 = 3x + 2*sqrt(3x) + 1Subtract to isolate: Subtract 3x and 1 from both sides to isolate the square root term. 5x + 1 - 3x - 1 = 2*sqrt(3x)Combine like terms: Combine like terms. 2x = 2*sqrt(3x)Divide to isolate: Divide both sides by 2 to isolate the square root. x = sqrt(3x)Square both sides again: Square both sides again to eliminate the square root. x^2 = (sqrt(3x))^2Apply squaring operation: Apply the squaring operation to both sides. x^2 = 3xSet equation to zero: Subtract 3x from both sides to set the equation to zero. x^2 - 3x = 0Factor out x: Factor out x from the left side of the equation. x(x - 3) = 0Apply zero product property: Apply the zero product property. x = 0 or x - 3 = 0Solve for x: Solve for x. x = 0 or x = 3Check solutions: Check the solutions in the original equation to ensure they do not produce a negative number under the square root or an incorrect equality. For x = 0: sqrt(5(0)+1)-1 = sqrt(3(0)) sqrt(1)-1 = sqrt(0) 1 - 1 = 0 0 = 0 (Valid solution)  For x = 3: sqrt(5(3)+1)-1 = sqrt(3(3)) sqrt(16)-1 = sqrt(9) 4 - 1 = 3 3 = 3 (Valid solution)  Both solutions are valid.

Solve the equation. $\newline$ $\sqrt{5 x+1}-1=\sqrt{3 x}$

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Solve the equation.\newline5x+1−1=3x \sqrt{5 x+1}-1=\sqrt{3 x}5x+1​−1=3x​

Solve the equation. $\newline$ $\sqrt{5 x+1}-1=\sqrt{3 x}$