What is factor 2/(2x-3)+x/(8x^2-10x-3) ?

The solution to factor 2/(2x-3)+x/(8x^2-10x-3) is (9x+2)/((2x-3)(4x+1))

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factor 2/(2x-3)+x/(8x^2-10x-3)

factor

\frac{2}{2 x - 3} + \frac{x}{8 x ^{2} - 10 x - 3}

\frac{9 x + 2}{( 2 x - 3 ) ( 4 x + 1 )}

Solution steps

\frac{2}{2 x - 3} + \frac{x}{8 x ^{2} - 10 x - 3}

Factor

8 x^{2} - 10 x - 3 : (4 x + 1) (2 x - 3)

= \frac{2}{2 x - 3} + \frac{x}{( 4 x + 1 ) ( 2 x - 3 )}

Least Common Multiplier of

2 x - 3, (4 x + 1) (2 x - 3) : (2 x - 3) (4 x + 1)

Adjust Fractions based on the LCM

= \frac{2 ( 4 x + 1 )}{( 2 x - 3 ) ( 4 x + 1 )} + \frac{x}{( 2 x - 3 ) ( 4 x + 1 )}

Since the denominators are equal, combine the fractions:

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

= \frac{2 ( 4 x + 1 ) + x}{( 2 x - 3 ) ( 4 x + 1 )}

Expand

2 (4 x + 1) + x : 9 x + 2

= \frac{9 x + 2}{( 2 x - 3 ) ( 4 x + 1 )}

- \frac{16}{8}

\frac{22 x y - 15 x ^{2} - 8 y ^{2}}{2 y - 3 x}

w^{2} - 30 w - 7 = 0

\frac{3}{5} (r + 10) = 12

2 x^{3} \cdot 2 x^{2}

What is factor 2/(2x-3)+x/(8x^2-10x-3) ?
The solution to factor 2/(2x-3)+x/(8x^2-10x-3) is (9x+2)/((2x-3)(4x+1))