Solve for x ax-bx/x+c = d, if a =/b+d

Answer:

dc/a-b-d

Step-by-step explanation:

ax – bx = d

x + c

Multiply both sides by x + c

ax – bx

(x + c) = d(x + c)

x + c

Simplify

ax – bx

(x+c): ax – bx

x + c

ax – bx = d(x+c)

Expand d(x+c): dx + cd

ax — bx = dx + cd

Subtract dx from both sides

ax – bx – dx = dx + cd – dx

Simplify

ax – bx – dx = cd

Factor ax – bx – dx: x(a – b – d)

x(a - b- d) = cd

Divide both sides by a – b – d; a + b + d

x(a – b - d) cd

a + b + d

a - b - d

a – b-d

Simplify

X =dc/a-b-d

The value of 'x' in the algebraic equation is  [tex]\rm x= \frac{dc}{a-b-d} \\[/tex]  where [tex]\rm a\neq b+d[/tex]

It is given that the algebraic equation  [tex]\rm \frac{ax-bx}{x+c}= d[/tex]

It is required to solve the algebraic (polynomial) equation if [tex]\rm a\neq b+d[/tex]

Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.

We have an algebraic equation:

[tex]\rm \frac{ax-bx}{x+c}= d[/tex]

[tex]\rm \frac{ax-bx}{x+c}= d\\\\\rm ax-bx=d(x+c)\\\rm ax-bx=dx+dc\\\rm ax-bx-dx=dc\\\rm (a-b-d)x=dc\\\\\rm x= \frac{dc}{a-b-d} \\[/tex]

Thus, the value of 'x' in the algebraic equation is  [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]

Learn more about Polynomial here:

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