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Multiply 2(x+3)/x(x-1)*4x(x+2)/10(x+3)
5 months ago
Q:
Multiply 2(x+3)/x(x-1)*4x(x+2)/10(x+3)
Accepted Solution
A:
Answer:(4 (x - 1) (x + 3)^2 (x + 2))/5Step-by-step explanation:Simplify the following: (2Γ4 x (x + 3) (x - 1) (x + 2) (x + 3))/(10 x) ((x - 1)Γ4Γ2 (x + 3) x (x + 2) (x + 3))/(xΓ10) = x/xΓ((x - 1)Γ4Γ2 (x + 3) (x + 2) (x + 3))/10 = ((x - 1)Γ4Γ2 (x + 3) (x + 2) (x + 3))/10: (4Γ2 (x - 1) (x + 3) (x + 2) (x + 3))/10 The gcd of 4 and 10 is 2, so ((x - 1)Γ4Γ2 (x + 3) (x + 2) (x + 3))/10 = ((2Γ2) 2 (x - 1) (x + 3) (x + 2) (x + 3))/(2Γ5) = 2/2Γ(2Γ2 (x - 1) (x + 3) (x + 2) (x + 3))/5 = (2Γ2 (x - 1) (x + 3) (x + 2) (x + 3))/5: (2Γ2 (x - 1) (x + 3) (x + 2) (x + 3))/5 Combine powers. (2Γ2 (x - 1) (x + 3) (x + 2) (x + 3))/5 = (2Γ2 (x - 1) (x + 3)^(1 + 1) (x + 2))/5: (2Γ2 (x + 3)^(1 + 1) (x - 1) (x + 2))/5 1 + 1 = 2: (2Γ2 (x - 1) (x + 3)^2 (x + 2))/5 2Γ2 = 4: Answer: (4 (x - 1) (x + 3)^2 (x + 2))/5