Answer:
m = (-3, 2) x = (-1)
Step-by-step explanation:
Just took this K12 test.
a) The resulting expression cannot factor
b) The solution to the given equation is {-1}
Given the expression [tex]\frac{6}{m+2} =\frac{m+3}{m-1}[/tex]
We are to find the value of m from the expression.
Cross multiply:
[tex]6(m-1) = (m+2)(m+3)\\6m-6=m^2+3m+2m+6\\6m-6=m^2+5m+6\\m^2+5m+6-6m+6=0\\m^2-m+12=0\\[/tex]
Factorize the result
[tex]m^2-m+12 =0\\[/tex]
[tex]m =\frac{1\pm\sqrt{1^1-4(12)} }{2}[/tex]
For the expression
[tex]\frac{x+3}{x+2} = 3 +\frac{1}{x} \\\frac{x+3}{x+2} =\frac{3x+1}{x}[/tex]
Cross multiply
[tex]x(x+3) = (x+2)(3x+1)\\x^2+3x = 3x^2+7x+2\\3x^2+7x+2-x^2-3x=0\\2x^2+4x+2=0\\x^2+2x+1=0[/tex]
Factorize the result
[tex]x^2+x+x+1=0\\x(x+1)+1(x+1) =0\\x+1 = 0 \\x = -1 \ twice[/tex]
This shows that the solution to the given equation is {-1}
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