What is ((x^2-1))/((sqrt(3x+1)-2)) ?

The solution to ((x^2-1))/((sqrt(3x+1)-2)) is ((x+1)(sqrt(3x+1)+2))/3

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simplify ((x^2-1))/((sqrt(3x+1)-2))

simplify

\frac{( x ^{2} - 1 )}{( 3 x + 1 - 2 )}

\frac{( x + 1 ) ( 3 x + 1 + 2 )}{3}

Solution steps

\frac{x ^{2} - 1}{3 x + 1 - 2}

Multiply by the conjugate

\frac{3 x + 1 + 2}{3 x + 1 + 2}

= \frac{( x ^{2} - 1 ) ( 3 x + 1 + 2 )}{( 3 x + 1 - 2 ) ( 3 x + 1 + 2 )}

(3 x + 1 - 2) (3 x + 1 + 2) = 3 x - 3

= \frac{( x ^{2} - 1 ) ( 3 x + 1 + 2 )}{3 x - 3}

Factor

x^{2} - 1 : (x + 1) (x - 1)

= \frac{( x + 1 ) ( x - 1 ) ( 3 x + 1 + 2 )}{3 x - 3}

Factor out common term

3

= \frac{( x + 1 ) ( x - 1 ) ( 3 x + 1 + 2 )}{3 ( x - 1 )}

Cancel the common factor:

x - 1

= \frac{( x + 1 ) ( 3 x + 1 + 2 )}{3}

\frac{( ( r ^{2} + h ^{2} ) ^{\frac{3}{2}} )}{( r ^{3} )}

(x + 1)^{2} (x + 1)

(7 x^{a + 2} + y) (7 x^{a + 2} + 5 y)

(1 + \frac{d ^{2}}{5} + 6 \frac{d}{5})^{- 1}

10 (x + 1) - 5 (x - 1.2) + 35

What is ((x^2-1))/((sqrt(3x+1)-2)) ?
The solution to ((x^2-1))/((sqrt(3x+1)-2)) is ((x+1)(sqrt(3x+1)+2))/3