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

The solution to (2x-1)/(2-x)+(x+3)/(2x+1) is (3x^2-x+5)/((-x+2)(2x+1))

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

simplify

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

\frac{3 x ^{2} - x + 5}{( - x + 2 ) ( 2 x + 1 )}

Solution steps

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

Least Common Multiplier of

2 - x, 2 x + 1 : (- x + 2) (2 x + 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

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

Simplify

(2 x - 1) (2 x + 1) + (x + 3) (- x + 2) : 3 x^{2} - x + 5

= \frac{3 x ^{2} - x + 5}{( - x + 2 ) ( 2 x + 1 )}

(x + 4) (x^{2} - 4 x + 16) + (5 - x) (25 + 5 x + x^{2})

\frac{m ^{2}}{m}

1 \frac{1}{4} \cdot 1 \frac{1}{4}

lo g_{2} (2147483648)

lo g_{5} (5) (5)^{\frac{1}{3}}

What is (2x-1)/(2-x)+(x+3)/(2x+1) ?
The solution to (2x-1)/(2-x)+(x+3)/(2x+1) is (3x^2-x+5)/((-x+2)(2x+1))