Respuesta :

JohnLayton
First, I'm going to write out the expression to make it easier to simplify. This expression is (4x^2 - 7x + 3)/(x^2 + 5x - 6). Now, we must factor both trinomials. Using the bottoms up method and the quadratic equation ((-b +/- sqrt(b^2 - 4ac))/2a), we can get an expression of ((x - 1)(4x - 3))/((x - 1)(x + 6)). Finally, we can cancel out the (x - 1) in the numerator with the (x - 1) in the denominator. This gives us a final expression of (4x - 3)/(x + 6).

Hope this helps!

Answer: Our simplified form :

[tex]\frac{4x-3}{x+6}[/tex]

Explanation:

Since we have given that

[tex]\frac{4x^2-7x+3}{x^2+5x-6}[/tex]

Now, we will simplify it step by step , we get

[tex]\frac{4x^2-4x-3x+3}{x^2-5x+x-6}\\\\=\frac{4x(x-1)-3(x-1)}{x(x+4)+1(x+4)}\\\\=\frac{(4x-3)(x-1)}{(x+4)(x+1)}\\\\=\frac{(4x-3)(x-1)}{(x-1)(x+6)}\\\\=\frac{4x-3}{x+6}[/tex]

Hence, our simplified form :

[tex]\frac{4x-3}{x+6}[/tex]

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