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For a!=0, which of the following expressions is equivalent to (-12a^(2)+96 a)/(-12a^(2)+60 a)" ? " Choose 1 answer: (A) (-a+8)/(-a-5) (B) (a+8)/(-a+5) (C) (-a+8)/(-a+5) (D) (-a+8a)/(-a+5a)

For a≠0 a \neq 0 , which of the following expressions is equivalent to −12a2+96a−12a2+60a \frac{-12 a^{2}+96 a}{-12 a^{2}+60 a} ?\newlineChoose 11 answer:\newline(A) −a+8−a−5 \frac{-a+8}{-a-5} \newline(B) a+8−a+5 \frac{a+8}{-a+5} \newline(C) −a+8−a+5 \frac{-a+8}{-a+5} \newline(D) −a+8a−a+5a \frac{-a+8 a}{-a+5 a}

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Full solution

Q. For a≠0 a \neq 0 , which of the following expressions is equivalent to −12a2+96a−12a2+60a \frac{-12 a^{2}+96 a}{-12 a^{2}+60 a} ?\newlineChoose 11 answer:\newline(A) −a+8−a−5 \frac{-a+8}{-a-5} \newline(B) a+8−a+5 \frac{a+8}{-a+5} \newline(C) −a+8−a+5 \frac{-a+8}{-a+5} \newline(D) −a+8a−a+5a \frac{-a+8 a}{-a+5 a}
  1. Simplify expression by factoring: Simplify the given expression by factoring out common terms in the numerator and the denominator.\newlineThe expression is (−12a2+96a)/(−12a2+60a)(-12a^{2}+96 a)/(-12a^{2}+60 a).\newlineFactor out −12a-12a from the numerator and −12a-12a from the denominator.\newlineThis gives us (−12a(a−8))/(−12a(a−5))(-12a(a - 8))/(-12a(a - 5)).
  2. Cancel out common terms: Cancel out the common terms in the numerator and the denominator.\newlineThe −12a-12a in the numerator and denominator cancel each other out.\newlineThis leaves us with (a−8)/(a−5)(a - 8)/(a - 5).
  3. Match with answer choices: Check the answer choices to see which one matches the simplified expression.\newlineThe simplified expression is (a−8)/(a−5)(a - 8)/(a - 5).\newlineComparing this with the answer choices, we see that it matches with choice (C) (−a+8)/(−a+5)(-a+8)/(-a+5).
  4. Verify sign consistency: Verify that the signs match with the simplified expression.\newlineThe expression (a−8)/(a−5)(a - 8)/(a - 5) can also be written as (−a+8)/(−a+5)(-a + 8)/(-a + 5) because multiplying the numerator and denominator by −1-1 does not change the value of the expression.

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