Question

simplify the rational expression.\\(\frac{x^{2}-\frac{1}{16}}{x^{2}-\frac{7}{12}x+\frac{1}{12}}\\)\
show your work here\
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simplify the rational expression.\\(\frac{b^{2}+\frac{16}{63}b+\frac{1}{63}}{b^{2}+\frac{14}{45}b+\frac{1}{45}}\\)

Explanation:

Step1: Eliminate denominators (1st expr)

Multiply numerator/denominator by 6:
$$\frac{6x^2 - 1}{6x^2 - 7x + 1}$$

Step2: Factor 1st expression

Factor numerator/denominator:
$$\frac{(2x-1)(3x+1)}{(3x-1)(2x-1)}$$

Step3: Cancel common terms (1st expr)

Cancel $(2x-1)$:
$$\frac{3x+1}{3x-1} \times \frac{6}{6} = \frac{6(2x-1)}{3x-1}$$

Step4: Eliminate denominators (2nd expr)

Multiply numerator/denominator by 45:
$$\frac{45b^2 + 30b + 1}{45b^2 + 14b + 1}$$

Step5: Factor 2nd expression

Factor numerator/denominator:
$$\frac{(3b+1)(15b+1)}{(9b+1)(5b+1)} \times \frac{15}{15} = \frac{15(3b+1)}{9b+1}$$

Step6: Cancel common terms (2nd expr)

Cancel $(5b+1)$:
$$\frac{15(3b+1)}{9b+1}$$

Answer:

1. $\frac{6(2x-1)}{3x-1}$
2. $\frac{15(3b+1)}{9b+1}$