ELIZABETH2703GO
Answered

Find the values for x for which the expression 2x-3/(x+4)(x-2) is equal to 1/5​

Answer :

CLARCH19GO

Answer:

1 and 7

Step-by-step explanation:

(x+4)(x-2) = x²+2x-8

set up proportion:

2x-3/ x²+2x-8 = 1/5

cross-multiply:

5(2x-3) = x²+2x-8

10x-15 = x²+2x-8

Combine Like Terms:

x²-8x+7

Factor:

(x-7)(x-1)

set each factor equal to zero and solve:  x = 1, x = 7

MAMYAMIRAHGO

Answer:

[tex] \frac{(2x - 3)}{(x + 4)(x - 2)} = \frac{1}{5} \\ \frac{2x - 3}{x {}^{2} - 2x + 4x - 8} = \frac{1}{5} \\ x {}^{2} - 2x + 4x - 8 = 5(2x - 3) \\ x {}^{2} + 2x - 8 = 10x - 15 \\ x {}^{2} + 2x - 10x = - 15 + 8 \\ x { }^{2} - 8x = - 7 \\ x {}^{2} - 8x + 7 = 0 \\ x {}^{2} - x - 7x + 7 = 0 \\ x(x - 1) + 7(x - 1) \\ x + 7 = 0 \\ x = - 7or \\ x - 1 = 0 \\ x = 1[/tex]

Step-by-step explanation:

x=7 or x=1

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