What can be the solution process for this

What can be the solution process for this


[tex]What can be the solution process for this[/tex]

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  1. x = 4/5

    Step-by-step explanation:

    We are given the equation:

    [tex]\displaystyle \large{ \frac{5x - 4}{ \sqrt{5x} + 2 } = 2 - \frac{ \sqrt{5x} + 2}{2} }[/tex]

    Multiply both sides by LCM which is 2(√5x +2) to clear out the denominator.

    [tex]\displaystyle \large{ \frac{5x - 4}{ \sqrt{5x} + 2 }(2)(\sqrt{5x} + 2)= 2 (2)( \sqrt{5x} + 2) - \frac{ \sqrt{5x} + 2}{2} (2)( \sqrt{5x + 2} )} \\ \displaystyle \large{ (5x - 4)2= 4( \sqrt{5x} + 2) - (\sqrt{5x} + 2)( \sqrt{5x} + 2)} \\ \displaystyle \large{ 10x - 8= 4\sqrt{5x} + 8 - ( \sqrt{5x} + 2) ^{2} } \\ \displaystyle \large{ 10x - 8= 4\sqrt{5x} + 8 - (5x + 4 \sqrt{5x} + 4) } \\ \displaystyle \large{ 10x - 8= 4\sqrt{5x} + 8 - 5x - 4 \sqrt{5x} - 4} \\ \displaystyle \large{ 10x - 8= 4 - 5x}[/tex]

    Thus, our simplified equation is;-

    [tex]\displaystyle \large{10x - 8 = 4 - 5x}[/tex]

    Add both sides by 5x then add both sides by 8.

    [tex]\displaystyle \large{10x + 5x - 8 = 4 - 5x + 5x} \\ \displaystyle \large{15x - 8 = 4} \\ \displaystyle \large{15x - 8 + 8 = 4 + 8} \\ \displaystyle \large{15x= 12}[/tex]

    Divide both sides by 15.

    [tex]\displaystyle \large{ \frac{15x}{15} = \frac{12}{15} } \\ \displaystyle \large{x = \frac{4}{5} }[/tex]

    Therefore, x = 4/5

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