Question

b. calculate each sum and difference

1. $\frac{x}{2}+\frac{7x}{6}$
2. $\frac{-2x}{5}-\frac{y}{10}+z$
3. $\frac{2x}{7}-\frac{y}{2}+\frac{x+1}{3}$
4. $\frac{2x}{5}+\frac{2x^{2}-1}{10}-\frac{4x+1}{6}$

Explanation:

Step1: Find common denominator (6)

$\frac{x}{2} = \frac{3x}{6}$

Step2: Add numerators

$\frac{3x}{6} + \frac{7x}{6} = \frac{3x+7x}{6} = \frac{10x}{6}$

Step3: Simplify the fraction

$\frac{10x}{6} = \frac{5x}{3}$

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Step1: Find common denominator (10)

$\frac{-2x}{5} = \frac{-4x}{10}$, $\frac{-y}{10}$ stays, $z = \frac{10z}{10}$

Step2: Combine terms

$\frac{-4x - y + 10z}{10}$

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Step1: Find common denominator (42)

$\frac{2x}{7} = \frac{12x}{42}$, $\frac{-y}{2} = \frac{-21y}{42}$, $\frac{x+1}{3} = \frac{14(x+1)}{42} = \frac{14x+14}{42}$

Step2: Combine numerators

$\frac{12x -21y +14x +14}{42} = \frac{26x -21y +14}{42}$

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Step1: Find common denominator (30)

$\frac{2x}{5} = \frac{12x}{30}$, $\frac{2x^2-1}{10} = \frac{6x^2-3}{30}$, $\frac{4x+1}{6} = \frac{20x+5}{30}$

Step2: Combine terms

$\frac{12x +6x^2 -3 -20x -5}{30}$

Step3: Simplify numerator

$\frac{6x^2 -8x -8}{30}$

Step4: Simplify the fraction

$\frac{3x^2 -4x -4}{15}$

Answer:

1. $\frac{5x}{3}$
2. $\frac{-4x - y + 10z}{10}$
3. $\frac{26x -21y +14}{42}$
4. $\frac{3x^2 -4x -4}{15}$