42 = 40(x-1) + 40
x-1 will be equal to the sales tax rate in this equation.
You can't make it proper.You can only simplify.
Step 1: Factor both the numerator and denominator down to prime factors:<span>62 = 2 * 31 </span>
40 = 23<span> * 5</span>Step 2: Calculate the greatest common factor, GCF (also called greatest common divisor, GCD), by taking all the common prime factors of the numerator and denominator, by the lowest powers:gcd(2 * 31; 23<span> * 5) = </span><span>2 </span>
Step 3: Divide both the numerator and denominator by their greatest common factor, GCF (also called the greatest common divisor, GCD):62/40 =
(2 * 31)/<span>(23 * 5)</span> =
<span>((2 * 31) : 2)</span> / <span>((23 * 5) : 2)</span> =
31/<span>(22 * 5)</span> =
31/20Step 4: Improper fraction, rewrite:<span>31 : 20 = 1 and remainder = 11 => </span>
31/20<span> = </span>(1 * 20 + 11)<span> / </span>20<span> = 1 + </span>11/20<span> = 1 </span>11/20<span> as a </span>mixed number (also called mixed fraction).<span>1 + 11 : 20 = 1.55 as a </span>decimal number<span>.</span>
Suppose the first integer is x, the second one is then x+1
reciprocals are 1/x and 1/(x+1)
1/x +1/(x+1)=-9/20
make the denominators the same:
1(x+1)/x(x+1) + 1x/x(x+1)=-9/20
simplify the demonstrator and add up the numerators: (2x+1)/(x^2+x)=-9/20
20(2x+1)=-9(x^2+x)
40x+20=-9x^2-9x
9x^2 +49x+20=0
factor: (1+5)(9x+4)=0
x=-5 or x=-4/9 (this one doesn't work because it is not an integer)
so the first integer is -5, the second integer is -4
Answer:
3 - 2√5
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2
Step-by-step explanation:
These two expressions have different denominators, and thus use of the LCD is necessary. The LCD is 4.
Thus, we have:
6/4 - (4/4)√5, or
6 - 4√5
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4
This can be reduced to:
3 - 2√5
------------- (answer)
2
