Question

iii. operations with rational expressions
a. calculate the least common denominator (lcd) for each sum and difference. describe any restriction(s) for the value of x.

1. $\frac{x}{3}+\frac{x+1}{15}$
2. $\frac{7x}{12}+\frac{x-2}{6}-\frac{x^2}{3}$
3. $\frac{x+1}{x}-\frac{x-1}{(x^2+x)}$
4. $\frac{3}{2x}+\frac{x^2+1}{4x^2+8}$

© carnegie learning, inc.

Explanation:

Step1: Factor denominators (Q2)

Denominators: $12=2^2\times3$, $6=2\times3$, $3=3$

Step2: Find LCD (Q2)

LCD is product of highest powers: $2^2\times3=12$

Step3: Check restrictions (Q2)

No variable in denominators, so no restrictions.

Step4: Factor denominators (Q3)

Denominators: $x$, $x^2+x=x(x+1)$

Step5: Find LCD (Q3)

LCD is $x(x+1)$

Step6: Find restrictions (Q3)

Set denominators ≠0: $x
eq0$, $x+1
eq0\implies x
eq-1$

Answer:

1. LCD: $12$; No restrictions on $x$
2. LCD: $x(x+1)$; Restrictions: $x

eq0$ and $x
eq-1$