Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x^2-1)/(x+2)=4x
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Equation 3*x+5+(x+5)=(1-x)+4
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Equation cos(x)=3/4
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Equation cos(x)=(1/2)
- Express {x} in terms of y where:
- 18*x-20*y=-7
- -13*x+7*y=11
- -19*x-14*y=-8
- -8*x-15*y=15
- Sum of series:
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2/9
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Identical expressions
- (x- one)/(five -x)= two / nine
- (x minus 1) divide by (5 minus x) equally 2 divide by 9
- (x minus one) divide by (five minus x) equally two divide by nine
- x-1/5-x=2/9
- (x-1) divide by (5-x)=2 divide by 9
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Similar expressions
- (x-1)/(5+x)=2/9
- x-1/5-x=2/9
- (x+2)/9=(x-3)/2
- (x+1)/(5-x)=2/9
- (6*x-1)/(5-x)=(6*x+3)/9+4/3
(x-1)/(5-x)=2/9 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\frac{x - 1}{5 - x} = \frac{2}{9}$$
Multiply the equation sides by the denominator 5 - x
we get:
$$\frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} = \frac{10}{9} - \frac{2 x}{9}$$
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without x)
from left part to right part, we given:
$$\frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} + 5 = \frac{55}{9} - \frac{2 x}{9}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{2 x}{9} + \frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} + 5 = \frac{55}{9}$$
Divide both parts of the equation by (5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x
We get the answer: x = 19/11
$$\frac{x - 1}{5 - x} = \frac{2}{9}$$
Multiply the equation sides by the denominator 5 - x
we get:
$$\frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} = \frac{10}{9} - \frac{2 x}{9}$$
Expand brackets in the left part
1+x5+x-5+x = 10/9 - 2*x/9
Looking for similar summands in the left part:
(1 - x)*(5 - x)/(-5 + x) = 10/9 - 2*x/9
Move free summands (without x)
from left part to right part, we given:
$$\frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} + 5 = \frac{55}{9} - \frac{2 x}{9}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{2 x}{9} + \frac{\left(1 - x\right) \left(5 - x\right)}{x - 5} + 5 = \frac{55}{9}$$
Divide both parts of the equation by (5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x
x = 55/9 / ((5 + 2*x/9 + (1 - x)*(5 - x)/(-5 + x))/x)
We get the answer: x = 19/11
Sum and product of roots
[src]
sum
19 -- 11
$$\frac{19}{11}$$
=
19 -- 11
$$\frac{19}{11}$$
product
19 -- 11
$$\frac{19}{11}$$
=
19 -- 11
$$\frac{19}{11}$$
19/11
The graph