# Solve Graphically -4/(2k+2)+7/(2k-2)=7/(4k^(2-4))

-42k+2+72k-2=74k2-4
Simplify -42k+2+72k-2.
Simplify each term.
Cancel the common factor of -4 and 2k+2.
Factor 2 out of -4.
2⋅-22k+2+72k-2=74k2-4
Cancel the common factors.
Factor 2 out of 2k.
2⋅-22(k)+2+72k-2=74k2-4
Factor 2 out of 2.
2⋅-22(k)+2(1)+72k-2=74k2-4
Factor 2 out of 2(k)+2(1).
2⋅-22(k+1)+72k-2=74k2-4
Cancel the common factor.
2⋅-22(k+1)+72k-2=74k2-4
Rewrite the expression.
-2k+1+72k-2=74k2-4
-2k+1+72k-2=74k2-4
-2k+1+72k-2=74k2-4
Move the negative in front of the fraction.
-2k+1+72k-2=74k2-4
Factor 2 out of 2k-2.
Factor 2 out of 2k.
-2k+1+72(k)-2=74k2-4
Factor 2 out of -2.
-2k+1+72(k)+2(-1)=74k2-4
Factor 2 out of 2(k)+2(-1).
-2k+1+72(k-1)=74k2-4
-2k+1+72(k-1)=74k2-4
-2k+1+72(k-1)=74k2-4
To write -2k+1 as a fraction with a common denominator, multiply by 2(k-1)2(k-1).
-2k+1⋅2(k-1)2(k-1)+72(k-1)=74k2-4
To write 72(k-1) as a fraction with a common denominator, multiply by k+1k+1.
-2k+1⋅2(k-1)2(k-1)+72(k-1)⋅k+1k+1=74k2-4
Write each expression with a common denominator of (k+1)⋅2(k-1), by multiplying each by an appropriate factor of 1.
Multiply 2k+1 and 2(k-1)2(k-1).
-2(2(k-1))(k+1)(2(k-1))+72(k-1)⋅k+1k+1=74k2-4
Multiply 72(k-1) and k+1k+1.
-2(2(k-1))(k+1)(2(k-1))+7(k+1)2(k-1)(k+1)=74k2-4
Reorder the factors of (k+1)(2(k-1)).
-2(2(k-1))2(k+1)(k-1)+7(k+1)2(k-1)(k+1)=74k2-4
Reorder the factors of 2(k-1)(k+1).
-2(2(k-1))2(k+1)(k-1)+7(k+1)2(k+1)(k-1)=74k2-4
-2(2(k-1))2(k+1)(k-1)+7(k+1)2(k+1)(k-1)=74k2-4
Combine the numerators over the common denominator.
-2(2(k-1))+7(k+1)2(k+1)(k-1)=74k2-4
Simplify the numerator.
Apply the distributive property.
-2(2k+2⋅-1)+7(k+1)2(k+1)(k-1)=74k2-4
Multiply 2 by -1.
-2(2k-2)+7(k+1)2(k+1)(k-1)=74k2-4
Apply the distributive property.
-2(2k)-2⋅-2+7(k+1)2(k+1)(k-1)=74k2-4
Multiply 2 by -2.
-4k-2⋅-2+7(k+1)2(k+1)(k-1)=74k2-4
Multiply -2 by -2.
-4k+4+7(k+1)2(k+1)(k-1)=74k2-4
Apply the distributive property.
-4k+4+7k+7⋅12(k+1)(k-1)=74k2-4
Multiply 7 by 1.
-4k+4+7k+72(k+1)(k-1)=74k2-4
Add -4k and 7k.
3k+4+72(k+1)(k-1)=74k2-4
Add 4 and 7.
3k+112(k+1)(k-1)=74k2-4
3k+112(k+1)(k-1)=74k2-4
3k+112(k+1)(k-1)=74k2-4
Simplify 74k2-4.
Move k2-4 to the numerator using the negative exponent rule 1b-n=bn.
3k+112(k+1)(k-1)=7k-(2-4)4
Simplify the numerator.
Subtract 4 from 2.
3k+112(k+1)(k-1)=7k–24
Multiply -1 by -2.
3k+112(k+1)(k-1)=7k24
3k+112(k+1)(k-1)=7k24
3k+112(k+1)(k-1)=7k24
Graph each side of the equation. The solution is the x-value of the point of intersection.
k≈-1.40672727,1.64031257
Solve Graphically -4/(2k+2)+7/(2k-2)=7/(4k^(2-4))

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