# Solve Graphically 4/(x^2+2x-8)+2/(x^2+x-6)=3/(x^2+7x+12)

4×2+2x-8+2×2+x-6=3×2+7x+12
Simplify each term.
Factor x2+2x-8 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -8 and whose sum is 2.
-2,4
Write the factored form using these integers.
4(x-2)(x+4)+2×2+x-6=3×2+7x+12
4(x-2)(x+4)+2×2+x-6=3×2+7x+12
Factor x2+x-6 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is 1.
-2,3
Write the factored form using these integers.
4(x-2)(x+4)+2(x-2)(x+3)=3×2+7x+12
4(x-2)(x+4)+2(x-2)(x+3)=3×2+7x+12
4(x-2)(x+4)+2(x-2)(x+3)=3×2+7x+12
Factor x2+7x+12 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 12 and whose sum is 7.
3,4
Write the factored form using these integers.
4(x-2)(x+4)+2(x-2)(x+3)=3(x+3)(x+4)
4(x-2)(x+4)+2(x-2)(x+3)=3(x+3)(x+4)
Graph each side of the equation. The solution is the x-value of the point of intersection.
x=-263
Solve Graphically 4/(x^2+2x-8)+2/(x^2+x-6)=3/(x^2+7x+12)