# Answer to Question #20104 in Trigonometry for Kristen Woods

Question #20104

adding and subtracting rational expressions

(x+2)/4 + (3x+1)/3

(x+2)/4 + (3x+1)/3

Expert's answer

Let's transform this expression using reduction to common denominator:

(x+2)/4 + (3x+1)/3 =

= (x+2)*3/(4*3) + (3x+1)*4/(3*4) =

= (3x+6)/12 + (12x+4)/12 =

= (3x+6+12x+4)/12 = (15x+10)/12.

Therefore,

(x+2)/4 + (3x+1)/3 = (15x+10)/12.

Also, we can rewrite obtained expression in the form of

(15x+10)/12 = 15x/12 + 10/12 = 5x/4 + 5/6.

(x+2)/4 + (3x+1)/3 =

= (x+2)*3/(4*3) + (3x+1)*4/(3*4) =

= (3x+6)/12 + (12x+4)/12 =

= (3x+6+12x+4)/12 = (15x+10)/12.

Therefore,

(x+2)/4 + (3x+1)/3 = (15x+10)/12.

Also, we can rewrite obtained expression in the form of

(15x+10)/12 = 15x/12 + 10/12 = 5x/4 + 5/6.

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