An equivalent expression with a rational denominator

Given the expression,

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

If we have , we will get by multiplying them. And .

So here in the problem, we will get,

Now in the numerator we have . We can check 8x is common there. we will take out -8x from it, we will get,

And in the denominator we have . We can check 2 is common there. If we take out 2 from it we will get,

So we can write the expression as

is common to the numerator and denominator both, if we cancel it we will get,

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

So we have got the required answer here.

The correct option is the last one.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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