Solve the equation algebraically. support your answer numerically and identify any extraneous solution4.)

1/x - 2/(x-3) = 4

multiply each side by x*(x-3)

x*(x-3)(1/x - 2/(x-3)) = 4*x*(x-3)

distribute

x*(x-3)(1/x) - 2/(x-3))x*(x-3) = 4*x*(x-3)

cancel

(x-3) - 2*x = 4x(x-3)

distribute

x-3-2x = 4x^2-12x

combine like terms

-x-3 = 4x^2 -12x

add x+3 to each side

0 = 4x^2 -12x+x+3

0 = 4x^2 -11x+3

using the quadratic formula

x= 11/8 - sqrt (73)/8

x=11/8 + sqrt (73)/8

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

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