Solve for x. 2/x^2−4 − 1/x+2=3/x−2 −32 −12 23 2
2 answers:
Answer:
Step-by-step explanation:
1. Multiply both sides of the equation by the LCM (x - 2)(x + 2):
factor x² - 4 by rewriting it as x² - 2²
x² - 2² = (x + 2)(x - 2)
now we have;
cancel the common factors (x - 2)(x + 2)
= 2
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cross cancel the common factor (x + 2)
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cross cancel the common factor (x - 2)
3(x + 2)
distribute the 3
3x + 6
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combining all new values, we have;
2 + (-x) + 2 = 3x + 6
-x + 4 = 3x + 6
2. Isolate x:
-x + 4-4 = 3x + 6-4
-x = 3x + 2
-x-3x = 3x-3x + 2
-4x = 2
-4x/-4 = 2/-4
x =
hope this helps!
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Answer:
Since a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Step-by-step explanation:
Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1
Since = a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.
Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb and
a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.
So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.