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Popular >

simplify ((x+ax)sqrt((x+ax)+1)-(xsqrt(x+1)))/(ax)

Solution

simplify

\frac{( x + a x ) ( x + a x ) + 1 - ( x x + 1 )}{a x}

Solution

\frac{x + a x + 1 + a x + a x + 1 - x + 1}{a}

Solution steps

\frac{( x + a x ) ( x + a x ) + 1 - ( x x + 1 )}{a x}

Simplify

(x + a x) (x + a x) + 1 - (x x + 1) : (x + a x) x + a x + 1 - x x + 1

= \frac{( x + a x ) x + a x + 1 - x x + 1}{a x}

Factor

(x + a x) x + a x + 1 - x x + 1 : x (x + a x + 1 + a x + a x + 1 - x + 1)

= \frac{x ( x + a x + 1 + a x + a x + 1 - x + 1 )}{a x}

Cancel the common factor:

x

= \frac{x + a x + 1 + a x + a x + 1 - x + 1}{a}

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Frequently Asked Questions (FAQ)

What is ((x+ax)sqrt((x+ax)+1)-(xsqrt(x+1)))/(ax) ?
The solution to ((x+ax)sqrt((x+ax)+1)-(xsqrt(x+1)))/(ax) is (sqrt(x+ax+1)+asqrt(x+ax+1)-sqrt(x+1))/a