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May someone help me with this factor equation?

May Someone Help Me With This Factor Equation class=

Sagot :

Answer:

[tex]\frac{x^2+8x+9}{(x+3)(x-1)}[/tex]

Step-by-step explanation:

[tex]\frac{2x}{x^2+2x-3}[/tex] + [tex]\frac{x+3}{x-1}[/tex] ← factor the denominator of first fraction

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

Before adding we require the denominators to be the same

Multiply numerator/denominator of second fraction by (x + 3)

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

Add the numerators leaving the common denominator ( LCD = (x + 3)(x - 1) )

= [tex]\frac{2x+(x+3)(x+3)}{(x+3)(x-1)}[/tex] ← expand factors on numerator using FOIL

= [tex]\frac{2x+x^2+6x+9}{(x+3)(x-1)}[/tex]

= [tex]\frac{x^2+8x+9}{(x+3)(x-1)}[/tex]