What is 1/x*(a/((a-x))-a/((a+3x)))-(3/((a+3x))) ?

The solution to 1/x*(a/((a-x))-a/((a+3x)))-(3/((a+3x))) is (4a)/((-x+a)(3x+a))-3/(a+3x)

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simplify 1/x*(a/((a-x))-a/((a+3x)))-(3/((a+3x)))

simplify

\frac{1}{x} \cdot (\frac{a}{( a - x )} - \frac{a}{( a + 3 x )}) - (\frac{3}{( a + 3 x )})

\frac{4 a}{( - x + a ) ( 3 x + a )} - \frac{3}{a + 3 x}

Solution steps

\frac{1}{x} (\frac{a}{a - x} - \frac{a}{a + 3 x}) - (\frac{3}{a + 3 x})

Apply rule:

- (a) = - a

- (\frac{3}{a + 3 x}) = - \frac{3}{a + 3 x}

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

Simplify

\frac{1}{x} (\frac{a}{a - x} - \frac{a}{a + 3 x}) : \frac{4 a x}{( - x + a ) ( 3 x + a ) x}

= \frac{4 a x}{( - x + a ) ( 3 x + a ) x} - \frac{3}{a + 3 x}

Cancel the common factor:

x

= \frac{4 a}{( - x + a ) ( 3 x + a )} - \frac{3}{a + 3 x}

(2 s^{4} + 5)^{5}

(x^{n} y^{- m})^{4} \cdot (x^{3} y^{- 2})^{- n}

\frac{( sin ( 14 x ) + a \cdot sin ( x ) )}{( 10 x ^{3} )}

(x^{3} - 3 x^{2} - 4 x)^{0.5}

(\frac{a}{3} - \frac{b}{5}) (\frac{3}{a} - \frac{5}{b})

What is 1/x*(a/((a-x))-a/((a+3x)))-(3/((a+3x))) ?
The solution to 1/x*(a/((a-x))-a/((a+3x)))-(3/((a+3x))) is (4a)/((-x+a)(3x+a))-3/(a+3x)