Two chords in a circle intersect. One chord is made of 6 and 5, and the other is made of x +1 and x. What is x?

x = 5 and -6

Step-by-step explanation:

Using the intersecting chord theorem which states that the products of the lengths of the line segments on each chord are equal.

Hence:

let

a = 6, b = 5, c = x+1 and d = x

Therefore, ab = cd

6*5 = x(x+1)

30 = x²+x

x²+x - 30 = 0

x²+ 6x - 5x - 30 = 0

x(x+6) - 5(x+6) =0

(x-5)(x+6) = 0

x-5 =0 and x+6 = 0

x = 5 and -6

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

step-by-step explanation:

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