Question 346812
(3x)/(2x-3)+(x)/(2x+3)

Multiply each term by a factor of 1 that will equate all the denominators.  In this case, all terms need a denominator of (2x-3)(2x+3). The (3x)/((2x-3)) expression needs to be multiplied by ((2x+3))/((2x+3)) to make the denominator (2x-3)(2x+3). The (x)/((2x+3)) expression needs to be multiplied by ((2x-3))/((2x-3)) to make the denominator (2x-3)(2x+3).
(3x)/(2x-3)*(2x+3)/(2x+3)+(x)/(2x+3)*(2x-3)/(2x-3)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (2x-3)(2x+3).
(3x(2x+3))/((2x-3)(2x+3))+(x)/(2x+3)*(2x-3)/(2x-3)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (2x-3)(2x+3).
(3x(2x+3))/((2x-3)(2x+3))+(x(2x-3))/((2x-3)(2x+3))

The numerators of expressions that have equal denominators can be combined.  In this case, (3x(2x+3))/((2x-3)(2x+3)) and ((x(2x-3)))/((2x-3)(2x+3)) have the same denominator of (2x-3)(2x+3), so the numerators can be combined.
(3x(2x+3)+(x(2x-3)))/((2x-3)(2x+3))

Simplify the numerator of the expression.
(6x^(2)+9x+2x^(2)-3x)/((2x-3)(2x+3))

Combine all similar terms in the polynomial 6x^(2)+9x+2x^(2)-3x.
(8x^(2)+6x)/((2x-3)(2x+3))

Factor out the GCF of 2x from each term in the polynomial.
(2x(4x)+2x(3))/((2x-3)(2x+3))

Factor out the GCF of 2x from 8x^(2)+6x.
(2x(4x+3))/((2x-3)(2x+3))