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Simplify the expression $3\left(\frac{x-2}{1-x}\right)-4\sqrt{\frac{x-2}{1-x}}+1$

Step-by-step Solution

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Solution

Final Answer

$\frac{-5+2x-4\sqrt{x-2}\sqrt{1-x}}{1-x}$
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Step-by-step Solution

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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$3\left(\frac{x-2}{1-x}\right)-4\left(\frac{\sqrt{x-2}}{\sqrt{1-x}}\right)+1$

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$3\left(\frac{x-2}{1-x}\right)-4\left(\frac{\sqrt{x-2}}{\sqrt{1-x}}\right)+1$

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Learn how to solve problems step by step online. Simplify the expression 3(x-2)/(1-x)-4((x-2)/(1-x))^1/2+1. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Multiplying the fraction by 3. Multiplying the fraction by -4. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

Final Answer

$\frac{-5+2x-4\sqrt{x-2}\sqrt{1-x}}{1-x}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind 3(x-2)/(1+-1x)+-4((x-2)/(1+-1x))^0.5 using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $\frac{-5+2x-4\sqrt{x-2}\sqrt{1-x}}{1-x}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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