Question:

Solve.
PLEASE HELP LOTS OF POINTS

x
x -1
=
x - 2
x - 3

x = 3/2 + sqrt(17)/2 or x = 3/2 - sqrt(17)/2

Step-by-step explanation:

Solve for x over the real numbers:

x/x - 1 = x - 3 - 2/x

x/x - 1 = 0:

0 = x - 3 - 2/x

0 = x - 3 - 2/x is equivalent to x - 3 - 2/x = 0:

x - 3 - 2/x = 0

Bring x - 3 - 2/x together using the common denominator x:

(x^2 - 3 x - 2)/x = 0

Multiply both sides by x:

x^2 - 3 x - 2 = 0

Add 2 to both sides:

x^2 - 3 x = 2

Add 9/4 to both sides:

x^2 - 3 x + 9/4 = 17/4

Write the left hand side as a square:

(x - 3/2)^2 = 17/4

Take the square root of both sides:

x - 3/2 = sqrt(17)/2 or x - 3/2 = -sqrt(17)/2

Add 3/2 to both sides:

x = 3/2 + sqrt(17)/2 or x - 3/2 = -sqrt(17)/2

Add 3/2 to both sides:

x = 3/2 + sqrt(17)/2 or x = 3/2 - sqrt(17)/2

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: