Question

Add $(3x^2-\frac{1}{5}x+\frac{7}{3})+(-\frac{1}{4}{x}^2+\frac{1}{3}x+\frac{1}{3}x-\frac{1}{6})+(-2x^2-\frac{1}{2}x+5)$

• A. $\frac{3x^2}{4}-\frac{11x}{30}+\frac{43}{6}$
• B. $\frac{3x^2}{2}-\frac{x}{6}+\frac{43}{6}$
• C. $\frac{3x^2}{4}+\frac{x}{30}+\frac{43}{6}$
• D. $\frac{3x^2}{4}-\frac{x}{30}-\frac{43}{6}$

Answer 1

The correct option is A $\frac{3x^2}{4}-\frac{11x}{30}+\frac{43}{6}$

To simplify an algebraic expression that consists of both like and unlike terms, we need to move the like terms together and then add or subtract their coefficients.

Here, the expression is $(3x^2-\frac{1}{5}x+\frac{7}{3})+(-\frac{1}{4}{x}^2+\frac{1}{3}x+\frac{1}{3}x-\frac{1}{6})+(-2x^2-\frac{1}{2}x+5)$ and we solve this as shown below:

$(3x^2-\frac{1}{5}x+\frac{7}{3})+(-\frac{1}{4}{x}^2+\frac{1}{3}x-\frac{1}{6})+(-2x^2-\frac{1}{2}x+5)=(3x^2-\frac{1}{4}{x}^2-2x^2)+(\frac{1}{3}x-\frac{1}{5}x-\frac{1}{2}x)+(5+\frac{7}{3}-\frac{1}{6})=x^2(3-\frac{1}{4}-2)+x(\frac{1}{3}-\frac{1}{5}-\frac{1}{2})+(5+\frac{7}{3}-\frac{1}{6})$

$=x^2\left(\frac{12-1-8}{4}\right)+x\left(\frac{10-6-15}{30}\right)+\left(\frac{30+14-1}{6}\right)\left(TakingLCM\right)=\frac{3x^2}{4}-\frac{11x}{30}+\frac{43}{6}$

Hence, $(3x^2-\frac{1}{5}x+\frac{7}{3})+(-\frac{1}{4}{x}^2+\frac{1}{3}x-\frac{1}{6})+(-2x^2-\frac{1}{2}x+5)=\frac{3x^2}{4}-\frac{11x}{30}+\frac{43}{6}$